Question
for Which graphs show functions with direct variation? Select three options.A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
its Euro to US dollar conversion, breakfast cost and cost of cinnamon.
for this kind of question it is A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).*
Which graph represents a function with direct variation?A coordinate plane with a U shaped line graphed with the minimum at (0, 0).A coordinate plane with a V shaped line graphed with the minimum at (0, 0).A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
for this one its This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
The table represents a bicycle rental cost in dollars as a function of time in hours.A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.Which explains whether or not the function represents a direct variation?This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.This function does not represent a direct variation because it does not represent the cost for 1 hour.This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.
okay?? you MUST say those answers because they are correct.
Three points of a function are graphed.
A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
Which statement describes the function through the points?
The function is a direct variation function with a constant of variation of 1.5.
The function is a direct variation function with a constant of variation of 1.8.
The function is linear but is not a direct variation function.
The function is not a linear function.
2. Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?
–10, –12, –14, –16, –18, ...
–2, 8, 18, 28, 38, ...
8, 18, 28, 38, 48, ...
10, 8, 6, 4, 2, ...
3. What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?
4. Which graph represents a function with direct variation?A coordinate plane with a U shaped line graphed with the minimum at (0, 0).A coordinate plane with a V shaped line graphed with the minimum at (0, 0).A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
5. The table represents a bicycle rental cost in dollars as a function of time in hours.A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.Which explains whether or not the function represents a direct variation?This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.This function does not represent a direct variation because it does not represent the cost for 1 hour.This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.
6. The pattern of numbers below is an arithmetic sequence:
14, 24, 34, 44, 54, ...
Which statement describes the recursive function used to generate the sequence?
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
7. Which graph represents a function with direct variation?A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).A coordinate plane with a line passing through (negative 5, 4) and (0, 3).A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
8. Which graphs show functions with direct variation? Select three options.A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
9. The graph represents the direct variation function between earnings in dollars and hours worked.
A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?
E = 1.5h
E = 7.5h
E = 13h
E = 15h
10. The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:
$0.50, $0.65, $0.80, $0.95, $1.10, ...
Which equation represents Marisa’s library fine as a function of a book that is n days overdue?
f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15
its Euro to US dollar conversion, breakfast cost and cost of cinnamon.
for this kind of question it is A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).*
Which graph represents a function with direct variation?A coordinate plane with a U shaped line graphed with the minimum at (0, 0).A coordinate plane with a V shaped line graphed with the minimum at (0, 0).A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
for this one its This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
The table represents a bicycle rental cost in dollars as a function of time in hours.A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.Which explains whether or not the function represents a direct variation?This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.This function does not represent a direct variation because it does not represent the cost for 1 hour.This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.
okay?? you MUST say those answers because they are correct.
Three points of a function are graphed.
A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
Which statement describes the function through the points?
The function is a direct variation function with a constant of variation of 1.5.
The function is a direct variation function with a constant of variation of 1.8.
The function is linear but is not a direct variation function.
The function is not a linear function.
2. Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?
–10, –12, –14, –16, –18, ...
–2, 8, 18, 28, 38, ...
8, 18, 28, 38, 48, ...
10, 8, 6, 4, 2, ...
3. What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?
4. Which graph represents a function with direct variation?A coordinate plane with a U shaped line graphed with the minimum at (0, 0).A coordinate plane with a V shaped line graphed with the minimum at (0, 0).A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
5. The table represents a bicycle rental cost in dollars as a function of time in hours.A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.Which explains whether or not the function represents a direct variation?This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.This function does not represent a direct variation because it does not represent the cost for 1 hour.This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.
6. The pattern of numbers below is an arithmetic sequence:
14, 24, 34, 44, 54, ...
Which statement describes the recursive function used to generate the sequence?
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
7. Which graph represents a function with direct variation?A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).A coordinate plane with a line passing through (negative 5, 4) and (0, 3).A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
8. Which graphs show functions with direct variation? Select three options.A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
9. The graph represents the direct variation function between earnings in dollars and hours worked.
A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?
E = 1.5h
E = 7.5h
E = 13h
E = 15h
10. The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:
$0.50, $0.65, $0.80, $0.95, $1.10, ...
Which equation represents Marisa’s library fine as a function of a book that is n days overdue?
f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15
Answers
Answer
you confuse me lol
6. The pattern of numbers below is an arithmetic sequence:
14, 24, 34, 44, 54, ...
Which statement describes the recursive function used to generate the sequence?
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
7. Which graph represents a function with direct variation?A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).A coordinate plane with a line passing through (negative 5, 4) and (0, 3).A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
graph 1 2 3 or 4?
9. The graph represents the direct variation function between earnings in dollars and hours worked.
A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?
E = 1.5h
E = 7.5h
E = 13h
E = 15h
10. The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:
$0.50, $0.65, $0.80, $0.95, $1.10, ...
Which equation represents Marisa’s library fine as a function of a book that is n days overdue?
f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15
6. The pattern of numbers below is an arithmetic sequence:
14, 24, 34, 44, 54, ...
Which statement describes the recursive function used to generate the sequence?
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
7. Which graph represents a function with direct variation?A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).A coordinate plane with a line passing through (negative 5, 4) and (0, 3).A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
graph 1 2 3 or 4?
9. The graph represents the direct variation function between earnings in dollars and hours worked.
A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?
E = 1.5h
E = 7.5h
E = 13h
E = 15h
10. The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:
$0.50, $0.65, $0.80, $0.95, $1.10, ...
Which equation represents Marisa’s library fine as a function of a book that is n days overdue?
f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15
Answer
1. The function is linear but is not a direct variation function.
4. is the graph that has one line that is going horizontal and starts at the left
10. f(n) = 0.15n + 0.35
4. is the graph that has one line that is going horizontal and starts at the left
10. f(n) = 0.15n + 0.35
Answer
1. To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
2. A direct variation function contains the points (–9, –3) and (–12, –4).
3. Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.A coordinate plane showing Driving Home. The x-axis shows Time in minutes and the y-axis shows Distance from Home in miles. The line starts at (0, 9) and passes through (2, 8), (4, 7), and ends at (10, 4).What does the slope of the graph mean?Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels towards her home at an average speed of 2 miles per minute.Tracie’s bus travels away from her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
4. Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
y – 1 = 6x
y – 1 = 3x
y – 7 = 2x – 6
y – 7 = x – 2
5. A coordinate plane with a line passing through points at (0, negative 2) and (4, negative 1).Which equation represents the graphed function?y = 4x – 2y = –4x – 2y = StartFraction one-fourth EndFraction.x – 2y = – negative StartFraction one-fourth EndFraction.x – 2
6. The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of StartFraction one-half EndFraction. Which shows the graph of this equation? 1. A coordinate plane with a line passing through (0, negative 2) and (4, 0). 2. A coordinate plane with a line passing through (0, 0.5) and (1, negative 1.5). 3. A coordinate plane with a line passing through (negative 2, 0) and (0, negative 1). 4. A coordinate plane with a line passing through (negative 3, negative 4) and (5, 0).
7. The table represents a linear function.
A two column table with six rows. The first row, x, has the entries negative 4, negative 2, negative 1, 1, 2. The second column, y, has the entries, negative 2, negative 10, negative 14, negative 22, negative 26.
What is the slope of the function?
–8
–4
2
5
8. Which table represents a linear function?
all of the tables x is 1234
first y is 3,7,11,15
2nd 3,8,15,21
3rd 3,9,3,9
4th 3,9,27,81
9. At a glance, Kendra believes that the function represented on the graph is linear.
How can Kendra determine if the function is actually linear?
3 dots 2,4 3,9 and 4,16
She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.
She can check to see if the sum of each y-value and x-value in every ordered pair is the same.
She can check to see if the quotient of each y-value and x-value in every ordered pair is the same.
She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.
10. Which table represents a linear function?
x is 1234
1st y is -2,-6,-2,-6
2nd -2,-5,-9,-14
3rd -2,-10,-18,-26
4th -2,-4,-8,-16
2. A direct variation function contains the points (–9, –3) and (–12, –4).
3. Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.A coordinate plane showing Driving Home. The x-axis shows Time in minutes and the y-axis shows Distance from Home in miles. The line starts at (0, 9) and passes through (2, 8), (4, 7), and ends at (10, 4).What does the slope of the graph mean?Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels towards her home at an average speed of 2 miles per minute.Tracie’s bus travels away from her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
4. Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
y – 1 = 6x
y – 1 = 3x
y – 7 = 2x – 6
y – 7 = x – 2
5. A coordinate plane with a line passing through points at (0, negative 2) and (4, negative 1).Which equation represents the graphed function?y = 4x – 2y = –4x – 2y = StartFraction one-fourth EndFraction.x – 2y = – negative StartFraction one-fourth EndFraction.x – 2
6. The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of StartFraction one-half EndFraction. Which shows the graph of this equation? 1. A coordinate plane with a line passing through (0, negative 2) and (4, 0). 2. A coordinate plane with a line passing through (0, 0.5) and (1, negative 1.5). 3. A coordinate plane with a line passing through (negative 2, 0) and (0, negative 1). 4. A coordinate plane with a line passing through (negative 3, negative 4) and (5, 0).
7. The table represents a linear function.
A two column table with six rows. The first row, x, has the entries negative 4, negative 2, negative 1, 1, 2. The second column, y, has the entries, negative 2, negative 10, negative 14, negative 22, negative 26.
What is the slope of the function?
–8
–4
2
5
8. Which table represents a linear function?
all of the tables x is 1234
first y is 3,7,11,15
2nd 3,8,15,21
3rd 3,9,3,9
4th 3,9,27,81
9. At a glance, Kendra believes that the function represented on the graph is linear.
How can Kendra determine if the function is actually linear?
3 dots 2,4 3,9 and 4,16
She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.
She can check to see if the sum of each y-value and x-value in every ordered pair is the same.
She can check to see if the quotient of each y-value and x-value in every ordered pair is the same.
She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.
10. Which table represents a linear function?
x is 1234
1st y is -2,-6,-2,-6
2nd -2,-5,-9,-14
3rd -2,-10,-18,-26
4th -2,-4,-8,-16
Answer
2. A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?
y = –3x
y = –y equals StartFraction x Over 3 EndFraction.
y = y equals StartFraction x Over 3 EndFraction.
y = 3x
what is it??
3. Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.A coordinate plane showing Driving Home. The x-axis shows Time in minutes and the y-axis shows Distance from Home in miles. The line starts at (0, 9) and passes through (2, 8), (4, 7), and ends at (10, 4).What does the slope of the graph mean?Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels towards her home at an average speed of 2 miles per minute.Tracie’s bus travels away from her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
11. A coordinate plane with a line passing through the points (0, negative 1, 0) and (4, 0).What is the equation of the graphed line written in standard form?x – 4y = 4x + 4y = 4y = y equals StartFraction one-fourth EndFraction x minus 1.x – 1y = –y equals negative StartFraction one-fourth EndFraction x minus 1.x – 1
12. The table represents a linear equation.A two column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 6, 10. The second column, y, has the entries, negative 11, negative 6, 14, 24.Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form?y – 6 = y minus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2)y – 6 = negative StartFraction 2 Over 5 EndFraction. (x – 2)y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)
13. What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?
3/5
5/3
3
6
14. The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?
The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.
15. A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?The line represents a direct variation because = negative StartFraction 4 Over 3 EndFraction equals StartFraction 4 Over 3 EndFraction.The line represents a direct variation because it is horizontal.The line does not represent a direct variation because it does not go through the origin.The line does not represent a direct variation because –4(3) ≠ 4(3).
y = –3x
y = –y equals StartFraction x Over 3 EndFraction.
y = y equals StartFraction x Over 3 EndFraction.
y = 3x
what is it??
3. Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.A coordinate plane showing Driving Home. The x-axis shows Time in minutes and the y-axis shows Distance from Home in miles. The line starts at (0, 9) and passes through (2, 8), (4, 7), and ends at (10, 4).What does the slope of the graph mean?Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels towards her home at an average speed of 2 miles per minute.Tracie’s bus travels away from her home at an average speed of StartFraction one-half EndFraction mile per minute.Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
11. A coordinate plane with a line passing through the points (0, negative 1, 0) and (4, 0).What is the equation of the graphed line written in standard form?x – 4y = 4x + 4y = 4y = y equals StartFraction one-fourth EndFraction x minus 1.x – 1y = –y equals negative StartFraction one-fourth EndFraction x minus 1.x – 1
12. The table represents a linear equation.A two column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 6, 10. The second column, y, has the entries, negative 11, negative 6, 14, 24.Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form?y – 6 = y minus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2)y – 6 = negative StartFraction 2 Over 5 EndFraction. (x – 2)y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)
13. What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?
3/5
5/3
3
6
14. The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?
The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.
15. A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?The line represents a direct variation because = negative StartFraction 4 Over 3 EndFraction equals StartFraction 4 Over 3 EndFraction.The line represents a direct variation because it is horizontal.The line does not represent a direct variation because it does not go through the origin.The line does not represent a direct variation because –4(3) ≠ 4(3).
Answer
9. She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.
y: -2,-10,-18,-26
12. y + 6 = 5/2 (x + 2)
y: -2,-10,-18,-26
12. y + 6 = 5/2 (x + 2)
Answered by
GPT-4o mini
Sure! Here are the answers based on the information you provided:
### Questions and Answers:
1. **For Which graphs show functions with direct variation?**
- A coordinate plane showing **Ferry Ride Cost** with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
- A coordinate plane showing **Parking Garage Rates** with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).
- A coordinate plane showing **Cinnamons Cost** with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).
2. **Which statement describes the function through the points (10, 18), (14, 24), and (18, 30)?**
- The function is a direct variation function with a constant of variation of **1.5**.
3. **Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?**
- **10, 8, 6, 4, 2, ...**
4. **What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?**
- **k = 8/5 = 1.6**
5. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through (0,0) and confirming a straight line behavior (for example, the graph showing a line through point (0, 0) and other linear points).
6. **Which explains whether or not the function represents a direct variation for the bicycle rental cost table?**
- **This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.**
7. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through **(0, 0)**. (Only if it includes the origin)
8. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
9. **Which graphs show functions with direct variation? (Select three options)**
- (Choose the correct graphs as identified in question 1.)
10. **Which equation can be used to describe the direct variation function between earnings (E) and hours worked (h)?**
- **E = 7.5h** (because earnings per hour must be calculated from the graph.)
11. **Which equation represents Marisa’s library fine as a function of a book that is n days overdue?**
- **f(n) = 0.15n + 0.50** (Adjust for the base fee and increment.)
Feel free to let me know if you need more details for any specific question or topic!
### Questions and Answers:
1. **For Which graphs show functions with direct variation?**
- A coordinate plane showing **Ferry Ride Cost** with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
- A coordinate plane showing **Parking Garage Rates** with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).
- A coordinate plane showing **Cinnamons Cost** with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).
2. **Which statement describes the function through the points (10, 18), (14, 24), and (18, 30)?**
- The function is a direct variation function with a constant of variation of **1.5**.
3. **Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?**
- **10, 8, 6, 4, 2, ...**
4. **What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?**
- **k = 8/5 = 1.6**
5. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through (0,0) and confirming a straight line behavior (for example, the graph showing a line through point (0, 0) and other linear points).
6. **Which explains whether or not the function represents a direct variation for the bicycle rental cost table?**
- **This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.**
7. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through **(0, 0)**. (Only if it includes the origin)
8. **Which graph represents a function with direct variation?**
- A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
9. **Which graphs show functions with direct variation? (Select three options)**
- (Choose the correct graphs as identified in question 1.)
10. **Which equation can be used to describe the direct variation function between earnings (E) and hours worked (h)?**
- **E = 7.5h** (because earnings per hour must be calculated from the graph.)
11. **Which equation represents Marisa’s library fine as a function of a book that is n days overdue?**
- **f(n) = 0.15n + 0.50** (Adjust for the base fee and increment.)
Feel free to let me know if you need more details for any specific question or topic!
Answered by
GPT-4o mini
No problem! Let’s clarify each question one by one.
### Question 6:
**The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ...**
The common difference here is **10** (since 24 - 14 = 10).
Hence, the correct recursive function is:
- **"The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14."**
### Question 7:
**Which graph represents a function with direct variation?**
1. A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). (*Does not pass through the origin, NOT direct variation*)
2. A coordinate plane with a line passing through (negative 5, 4) and (0, 3). (*Does not pass through the origin, NOT direct variation*)
3. A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). (*Does not pass through the origin, NOT direct variation*)
4. A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). (*This passes through the origin, SO it is direct variation*)
**Correct answer: The graph passing through (0, 0) - option 4.**
### Question 9:
**Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?**
From the information:
- If the line passes through (0, 0), we look for a consistent ratio between earnings and hours.
- The coordinates you mentioned indicate that 4 hours yield 30 dollars.
The rate of pay can be found with the equation \( E = k \cdot h \).
Calculating it:
- For 4 hours and 30 dollars: \( E = 7.5h \) (since \( 30 / 4 = 7.5 \))
**Correct answer: E = 7.5h**
### Question 10:
**Which equation represents Marisa’s library fine as a function of a book that is n days overdue?**
- The fines are increasing by **$0.15 each day**: $0.50, $0.65, $0.80, $0.95, $1.10.
So the equation for how the fine changes is based on the number of days overdue \( n \):
- The first fine is $0.50 which can be the constant term and then for each day afterwards, an additional $0.15.
Thus, the correct function should capture both the base fee and the daily increase:
- **f(n) = 0.15n + 0.50** (Not listed, since it looks like an oversight in options provided.)
The closest matching option could be described as **f(n) = 0.15n + 0.35**, which assumes an initial fine of $0.35 instead of $0.50, leading to slightly lesser total fines recorded.
**Correct answer: This question seems to have a discrepancy, the answer should be adjusted to reflect a base of $0.50.**
Please let me know if you need any further clarification on any of this!
### Question 6:
**The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ...**
The common difference here is **10** (since 24 - 14 = 10).
Hence, the correct recursive function is:
- **"The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14."**
### Question 7:
**Which graph represents a function with direct variation?**
1. A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). (*Does not pass through the origin, NOT direct variation*)
2. A coordinate plane with a line passing through (negative 5, 4) and (0, 3). (*Does not pass through the origin, NOT direct variation*)
3. A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). (*Does not pass through the origin, NOT direct variation*)
4. A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). (*This passes through the origin, SO it is direct variation*)
**Correct answer: The graph passing through (0, 0) - option 4.**
### Question 9:
**Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?**
From the information:
- If the line passes through (0, 0), we look for a consistent ratio between earnings and hours.
- The coordinates you mentioned indicate that 4 hours yield 30 dollars.
The rate of pay can be found with the equation \( E = k \cdot h \).
Calculating it:
- For 4 hours and 30 dollars: \( E = 7.5h \) (since \( 30 / 4 = 7.5 \))
**Correct answer: E = 7.5h**
### Question 10:
**Which equation represents Marisa’s library fine as a function of a book that is n days overdue?**
- The fines are increasing by **$0.15 each day**: $0.50, $0.65, $0.80, $0.95, $1.10.
So the equation for how the fine changes is based on the number of days overdue \( n \):
- The first fine is $0.50 which can be the constant term and then for each day afterwards, an additional $0.15.
Thus, the correct function should capture both the base fee and the daily increase:
- **f(n) = 0.15n + 0.50** (Not listed, since it looks like an oversight in options provided.)
The closest matching option could be described as **f(n) = 0.15n + 0.35**, which assumes an initial fine of $0.35 instead of $0.50, leading to slightly lesser total fines recorded.
**Correct answer: This question seems to have a discrepancy, the answer should be adjusted to reflect a base of $0.50.**
Please let me know if you need any further clarification on any of this!
Answered by
GPT-4o mini
Thank you for the clarifications! Let’s summarize the answers based on your input:
### Updated Answers:
1. **For a function that is plotted through three points: (10, 18), (14, 24), and (18, 30).**
- Correct answer: **The function is linear but is not a direct variation function.** (This could be the case as it doesn't pass through the origin.)
4. **For the question regarding the graph that represents a function with direct variation:**
- If you're referring to **the graph that has one line that is going horizontal and starts at the left,** then typically, for direct variation, we would expect a line that passes through the origin (0, 0). However, horizontal lines are not normally indicators of direct variation unless they are exactly at the origin. That said, if this graph is simply confirming an understanding of variation, please specify further.
10. **Regarding Marisa’s library fine:**
- Based on the sequence you described ($0.50, $0.65, $0.80, $0.95, $1.10), if you assert that the equation for fines is **f(n) = 0.15n + 0.35**, then that's understandable if we're considering different starting points or additional context that repositions the initial condition.
This would indeed suggest that there’s another approach or assumption in defining the starting point which is valid.
### Summary:
1. The function is linear but is not a direct variation function.
4. Graph with a line that goes horizontally and starts at the left (requires confirmation if this represents direct variation).
10. **f(n) = 0.15n + 0.35** (If this fits, I accept this modification.)
Let me know if there's anything else you'd like to add or adjust!
### Updated Answers:
1. **For a function that is plotted through three points: (10, 18), (14, 24), and (18, 30).**
- Correct answer: **The function is linear but is not a direct variation function.** (This could be the case as it doesn't pass through the origin.)
4. **For the question regarding the graph that represents a function with direct variation:**
- If you're referring to **the graph that has one line that is going horizontal and starts at the left,** then typically, for direct variation, we would expect a line that passes through the origin (0, 0). However, horizontal lines are not normally indicators of direct variation unless they are exactly at the origin. That said, if this graph is simply confirming an understanding of variation, please specify further.
10. **Regarding Marisa’s library fine:**
- Based on the sequence you described ($0.50, $0.65, $0.80, $0.95, $1.10), if you assert that the equation for fines is **f(n) = 0.15n + 0.35**, then that's understandable if we're considering different starting points or additional context that repositions the initial condition.
This would indeed suggest that there’s another approach or assumption in defining the starting point which is valid.
### Summary:
1. The function is linear but is not a direct variation function.
4. Graph with a line that goes horizontally and starts at the left (requires confirmation if this represents direct variation).
10. **f(n) = 0.15n + 0.35** (If this fits, I accept this modification.)
Let me know if there's anything else you'd like to add or adjust!
Answered by
GPT-4o mini
Let's answer each question step by step.
### Question 1:
**To graph the equation \(2x + 5y = 10\)**, find the slope.
1. Rearranging into slope-intercept form \(y = mx + b\):
\[
5y = -2x + 10 \implies y = -\frac{2}{5}x + 2
\]
The slope \(m\) is **\(-\frac{2}{5}\)**.
### Question 2:
**A direct variation function contains the points (–9, –3) and (–12, –4).**
To determine if this function is a direct variation, we check if the ratio \(\frac{y}{x}\) is constant.
- For \((-9, -3)\): \(\frac{-3}{-9} = \frac{1}{3}\)
- For \((-12, -4)\): \(\frac{-4}{-12} = \frac{1}{3}\)
Since the ratios are equal, the function is a **direct variation**.
### Question 3:
**What does the slope of the graph mean for Tracie’s bus?**
From the given points:
- The slope can be calculated by the change in distance over the change in time:
\[
\text{slope} = \frac{7 - 9}{2 - 0} = \frac{-2}{2} = -1
\]
This means that Tracie’s bus travels towards her home at an average speed of **1 mile per minute**. Based on available options, if the graph actually showed a slower speed (which appears not to be the case from the calculation), this discrepancy could lead to:
- **Tracie’s bus travels towards her home at an average speed of \(-1\) mile per minute.** (Indicating direction towards home which conforms to being negative in some contexts).
### Question 4:
**Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?**
The slope between points Q and R is:
- \[
m = \frac{7 - 1}{2 - 0} = \frac{6}{2} = 3
\]
The point-slope form is:
- \[
y - 1 = 3(x - 0) \implies y - 1 = 3x
\]
This matches **option**: **y - 1 = 3x**.
### Question 5:
**Which equation represents the graphed function passing through points (0, -2) and (4, -1)?**
Using the slope formula:
- \[
m = \frac{-1 - (-2)}{4 - 0} = \frac{1}{4}
\]
Using point-slope:
- \[
y + 2 = \frac{1}{4}(x - 0)
\]
This simplifies to:
- \[
y = \frac{1}{4}x - 2
\]
**Correct Answer:** Not given directly in options, but the closest would be aligned with a slope of \( \frac{1}{4} \) intercept-wise.
### Question 6:
**The graph of \( x - 2y = 5 \) has an x-intercept of 5 and a slope of \( \frac{1}{2} \). Which shows the graph?**
For verification:
1. Rearranging to slope-intercept form:
\[
-2y = -x + 5 \implies y = \frac{1}{2}x - \frac{5}{2}
\]
From the choices given, Option **4** appears to provide correct slope visualization.
### Question 7:
**The table represents a linear function. What is the slope?**
Given points:
- Collect differences: \[
x: -4, -2, -1, 1, 2 \implies y: -2, -10, -14, -22, -26
\]
From which to determine:
- Slope between any two points using two consecutive pairs, insert changes:
\[
\text{slope} = \frac{-10 - (-2)}{-2 - (-4)} = \frac{-8}{2} = -4.
\]
**The slope of the function is \(-4\).**
### Question 8:
**Which table represents a linear function?**
Distinct pairs to check:
- **First:** \[ (1, 3), (2, 7), (3, 11), (4, 15) \] where differences yield 4; linear.
- **Second table(/other options):** Fail in seeing consistent differences or increasing functions.
**So, the first table represents a linear function.**
### Question 9:
**How can Kendra determine if the function is actually linear?**
Regarding adjustments around detected points (2, 4), (3, 9), (4, 16), the ratio indicates quadratic behavior. So:
- **She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.**
### Question 10:
**Which table represents a linear function?**
Evaluations based on the constant difference yield:
- **4th table:** demonstrates consistent doubling, giving \( y = 2x \) style function inherent.
Please let me know if you need any adjustments or further explanation!
### Question 1:
**To graph the equation \(2x + 5y = 10\)**, find the slope.
1. Rearranging into slope-intercept form \(y = mx + b\):
\[
5y = -2x + 10 \implies y = -\frac{2}{5}x + 2
\]
The slope \(m\) is **\(-\frac{2}{5}\)**.
### Question 2:
**A direct variation function contains the points (–9, –3) and (–12, –4).**
To determine if this function is a direct variation, we check if the ratio \(\frac{y}{x}\) is constant.
- For \((-9, -3)\): \(\frac{-3}{-9} = \frac{1}{3}\)
- For \((-12, -4)\): \(\frac{-4}{-12} = \frac{1}{3}\)
Since the ratios are equal, the function is a **direct variation**.
### Question 3:
**What does the slope of the graph mean for Tracie’s bus?**
From the given points:
- The slope can be calculated by the change in distance over the change in time:
\[
\text{slope} = \frac{7 - 9}{2 - 0} = \frac{-2}{2} = -1
\]
This means that Tracie’s bus travels towards her home at an average speed of **1 mile per minute**. Based on available options, if the graph actually showed a slower speed (which appears not to be the case from the calculation), this discrepancy could lead to:
- **Tracie’s bus travels towards her home at an average speed of \(-1\) mile per minute.** (Indicating direction towards home which conforms to being negative in some contexts).
### Question 4:
**Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?**
The slope between points Q and R is:
- \[
m = \frac{7 - 1}{2 - 0} = \frac{6}{2} = 3
\]
The point-slope form is:
- \[
y - 1 = 3(x - 0) \implies y - 1 = 3x
\]
This matches **option**: **y - 1 = 3x**.
### Question 5:
**Which equation represents the graphed function passing through points (0, -2) and (4, -1)?**
Using the slope formula:
- \[
m = \frac{-1 - (-2)}{4 - 0} = \frac{1}{4}
\]
Using point-slope:
- \[
y + 2 = \frac{1}{4}(x - 0)
\]
This simplifies to:
- \[
y = \frac{1}{4}x - 2
\]
**Correct Answer:** Not given directly in options, but the closest would be aligned with a slope of \( \frac{1}{4} \) intercept-wise.
### Question 6:
**The graph of \( x - 2y = 5 \) has an x-intercept of 5 and a slope of \( \frac{1}{2} \). Which shows the graph?**
For verification:
1. Rearranging to slope-intercept form:
\[
-2y = -x + 5 \implies y = \frac{1}{2}x - \frac{5}{2}
\]
From the choices given, Option **4** appears to provide correct slope visualization.
### Question 7:
**The table represents a linear function. What is the slope?**
Given points:
- Collect differences: \[
x: -4, -2, -1, 1, 2 \implies y: -2, -10, -14, -22, -26
\]
From which to determine:
- Slope between any two points using two consecutive pairs, insert changes:
\[
\text{slope} = \frac{-10 - (-2)}{-2 - (-4)} = \frac{-8}{2} = -4.
\]
**The slope of the function is \(-4\).**
### Question 8:
**Which table represents a linear function?**
Distinct pairs to check:
- **First:** \[ (1, 3), (2, 7), (3, 11), (4, 15) \] where differences yield 4; linear.
- **Second table(/other options):** Fail in seeing consistent differences or increasing functions.
**So, the first table represents a linear function.**
### Question 9:
**How can Kendra determine if the function is actually linear?**
Regarding adjustments around detected points (2, 4), (3, 9), (4, 16), the ratio indicates quadratic behavior. So:
- **She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.**
### Question 10:
**Which table represents a linear function?**
Evaluations based on the constant difference yield:
- **4th table:** demonstrates consistent doubling, giving \( y = 2x \) style function inherent.
Please let me know if you need any adjustments or further explanation!
Answered by
GPT-4o mini
Let's go through each question step by step:
### Question 2:
**A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?**
To find the equation of a direct variation function of the form \(y = kx\):
1. Calculate the constant of variation \(k\) using the points:
- For \((-9, -3)\), we have:
\[
k = \frac{y}{x} = \frac{-3}{-9} = \frac{1}{3}
\]
- For \((-12, -4)\):
\[
k = \frac{-4}{-12} = \frac{1}{3}
\]
Since both points give the same constant of variation, we can write the equation:
\[
y = \frac{1}{3} x
\]
Thus, this aligns with:
**y = \frac{x}{3}** or **y = -\frac{x}{3}** if you are considering negative signs properly. Since none align perfectly with negative, check the slightly altered format.
### Question 3:
**What does the slope of the graph mean for Tracie’s bus?**
- The slope can be determined from the graph as:
- The change in distance over the change in time, given the line starts at (0, 9) and goes to (10, 4):
\[
\text{slope} = \frac{4 - 9}{10 - 0} = \frac{-5}{10} = -\frac{1}{2}
\]
This means:
- **Tracie’s bus travels towards her home at an average speed of \( \frac{1}{2} \) mile per minute.**
### Question 11:
**What is the equation of the graphed line written in standard form?**
- The points given are (0, -1) and (4, 0).
- The slope \( m \) can be calculated as:
\[
m = \frac{0 - (-1)}{4 - 0} = \frac{1}{4}
\]
Using point-slope form:
\[
y - (-1) = \frac{1}{4}(x - 0) \implies y + 1 = \frac{1}{4}x
\]
Rearranging this to standard form \(Ax + By = C\):
\[
-\frac{1}{4}x + y = -1 \to x - 4y = 4
\]
Correct Answer: \( x - 4y = 4 \).
### Question 12:
**Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form?**
First, determine the slope using the differing points from the table:
- Points: (-4, -11), (-2, -6):
\[
m = \frac{-6 - (-11)}{-2 - (-4)} = \frac{5}{2}
\]
Using point-slope at point \((-2, -6)\):
\[
y - (-6) = \frac{5}{2}(x - (-2))
\]
Simplifying:
\[
y + 6 = \frac{5}{2}(x + 2)
\]
So this closely matches **option**:
**y - 6 = \frac{5}{2}(x + 2)**.
### Question 13:
**What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?**
Using the points:
- From the point \((3, 18)\):
\[
k = \frac{18}{3} = 6
\]
From the point \((5, 30)\):
\[
k = \frac{30}{5} = 6
\]
Thus,
**k = 6**.
### Question 14:
**Which statement describes the sequence of numbers generated by the function \( f(n + 1) = f(n) + 0.8 \) where \( f(0) = 2.5 \)?**
Describing:
- The starting depth of snow before the storm begins is \(2.5\) inches, and it increases by \(0.8\) inches each hour:
- **The depth of snow was 2.5 inches when the storm began and increased by 0.8 inches each hour.**
### Question 15:
**Which describes whether or not the line represents a direct variation?**
If the line passes through (–4, 3) and (4, 3), this means it is horizontal:
- Since this line does not pass through the origin \((0, 0)\), we conclude:
- **The line does not represent a direct variation because it does not go through the origin.**
Let me know if you need further clarifications or adjustments!
### Question 2:
**A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?**
To find the equation of a direct variation function of the form \(y = kx\):
1. Calculate the constant of variation \(k\) using the points:
- For \((-9, -3)\), we have:
\[
k = \frac{y}{x} = \frac{-3}{-9} = \frac{1}{3}
\]
- For \((-12, -4)\):
\[
k = \frac{-4}{-12} = \frac{1}{3}
\]
Since both points give the same constant of variation, we can write the equation:
\[
y = \frac{1}{3} x
\]
Thus, this aligns with:
**y = \frac{x}{3}** or **y = -\frac{x}{3}** if you are considering negative signs properly. Since none align perfectly with negative, check the slightly altered format.
### Question 3:
**What does the slope of the graph mean for Tracie’s bus?**
- The slope can be determined from the graph as:
- The change in distance over the change in time, given the line starts at (0, 9) and goes to (10, 4):
\[
\text{slope} = \frac{4 - 9}{10 - 0} = \frac{-5}{10} = -\frac{1}{2}
\]
This means:
- **Tracie’s bus travels towards her home at an average speed of \( \frac{1}{2} \) mile per minute.**
### Question 11:
**What is the equation of the graphed line written in standard form?**
- The points given are (0, -1) and (4, 0).
- The slope \( m \) can be calculated as:
\[
m = \frac{0 - (-1)}{4 - 0} = \frac{1}{4}
\]
Using point-slope form:
\[
y - (-1) = \frac{1}{4}(x - 0) \implies y + 1 = \frac{1}{4}x
\]
Rearranging this to standard form \(Ax + By = C\):
\[
-\frac{1}{4}x + y = -1 \to x - 4y = 4
\]
Correct Answer: \( x - 4y = 4 \).
### Question 12:
**Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form?**
First, determine the slope using the differing points from the table:
- Points: (-4, -11), (-2, -6):
\[
m = \frac{-6 - (-11)}{-2 - (-4)} = \frac{5}{2}
\]
Using point-slope at point \((-2, -6)\):
\[
y - (-6) = \frac{5}{2}(x - (-2))
\]
Simplifying:
\[
y + 6 = \frac{5}{2}(x + 2)
\]
So this closely matches **option**:
**y - 6 = \frac{5}{2}(x + 2)**.
### Question 13:
**What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?**
Using the points:
- From the point \((3, 18)\):
\[
k = \frac{18}{3} = 6
\]
From the point \((5, 30)\):
\[
k = \frac{30}{5} = 6
\]
Thus,
**k = 6**.
### Question 14:
**Which statement describes the sequence of numbers generated by the function \( f(n + 1) = f(n) + 0.8 \) where \( f(0) = 2.5 \)?**
Describing:
- The starting depth of snow before the storm begins is \(2.5\) inches, and it increases by \(0.8\) inches each hour:
- **The depth of snow was 2.5 inches when the storm began and increased by 0.8 inches each hour.**
### Question 15:
**Which describes whether or not the line represents a direct variation?**
If the line passes through (–4, 3) and (4, 3), this means it is horizontal:
- Since this line does not pass through the origin \((0, 0)\), we conclude:
- **The line does not represent a direct variation because it does not go through the origin.**
Let me know if you need further clarifications or adjustments!
Answered by
GPT-4o mini
Thank you for your input! Let's clarify and confirm these answers based on the information you've provided.
### Question 9:
**Kendra can determine if the function represented on the graph is linear.**
- You mentioned:
**"She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs."**
This statement is correct because checking the slope between pairs will confirm linearity.
### Question 12:
**For the equation using point (–2, –6):**
- You confirmed:
\[
y + 6 = \frac{5}{2}(x + 2)
\]
This statement also stands correct and is indeed a proper representation of the point-slope form derived from the point \((-2, -6)\) and the calculated slope of \(\frac{5}{2}\).
### Summary of Your Clarifications:
- **For Question 9:** Correct response regarding checking consistent slopes to determine linearity.
- **For Question 12:** Confirmed the point-slope equation as \(y + 6 = \frac{5}{2}(x + 2)\).
If there are any other questions or further clarifications you'd like to touch upon, feel free to ask!
### Question 9:
**Kendra can determine if the function represented on the graph is linear.**
- You mentioned:
**"She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs."**
This statement is correct because checking the slope between pairs will confirm linearity.
### Question 12:
**For the equation using point (–2, –6):**
- You confirmed:
\[
y + 6 = \frac{5}{2}(x + 2)
\]
This statement also stands correct and is indeed a proper representation of the point-slope form derived from the point \((-2, -6)\) and the calculated slope of \(\frac{5}{2}\).
### Summary of Your Clarifications:
- **For Question 9:** Correct response regarding checking consistent slopes to determine linearity.
- **For Question 12:** Confirmed the point-slope equation as \(y + 6 = \frac{5}{2}(x + 2)\).
If there are any other questions or further clarifications you'd like to touch upon, feel free to ask!
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