Question
Which linear graph represents a proportional relationship?
Group of answer choices
a graph of a line that passes through the points 0 comma 4 and 2 comma 0
a graph of a line that passes through the points 0 comma negative 3 and 1 comma negative 1
a graph of a line that passes through the points 0 comma 0 and 1 comma 6
a graph of a line that passes through the points 0 comma negative 1 and 2 comma negative 1
Flag question: Question 2
Question 22 pts
M08.B-E.2.1.1
Lesson 1
Which of the following tables represents a linear relationship that is also proportional?
Group of answer choices
x 3 1 −1
y −2 0 2
x 6 3 0
y −2 −1 0
x 0 1 2
y −1 0 1
x −4 −2 0
y 0 2 4
Flag question: Question 3
Question 32 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the distance, y, that a car traveled in x hours:
A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to 225 in increments of 45 for each grid line. A line is shown connecting ordered pairs 1, 45 and 2, 90 and 3, 135 and 4, 180. The title of the graph is Rate of Travel.
What is the rate of change (slope) for the relationship represented in the graph?
Group of answer choices
fraction 1 over 90
fraction 1 over 45
90
45
Flag question: Question 4
Question 42 pts
M08.B-E.2.1.3
Lesson 2
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x axis and Distance from Island in miles labeled on y axis. The scale on the x axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
What is the speed of the motorboat?
Group of answer choices
50 miles per hour
75 miles per hour
25 miles per hour
225 miles per hour
Flag question: Question 5
Question 52 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the number of paintballs a machine launches, y, in x seconds:
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line. A line is shown connecting points on ordered pair 2, 12 and 4, 24 and 6, 36 and 8, 48.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
Group of answer choices
fraction 2 over 12
fraction 12 over 2
fraction 2 over 48
fraction 48 over 2
Flag question: Question 6
Question 62 pts
M08.B-E.2.1.1
Lesson 2
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,240 and 4,320 and 5,400 and 6,480. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 450 in increments of 90 for each grid line. A line passing through the ordered pairs 2, 90 and 4, 180 and 6, 270 and 8, 360 is drawn.
Which statement correctly compares the rates (slopes) of these representations?
Group of answer choices
The rate of the table is greater than the rate of the graph.
The rates of the table and the graph are the same.
The rate of the graph is greater than the rate of the table.
Flag question: Question 7
Question 72 pts
M08.B-E.2.1.2
Lesson 3
The figure shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 15 to positive 15 in increments of 3 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 12, negative 4, and 0, 0, and 12, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to negative 6, negative 2 labeled A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 6, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 6, negative 2 to negative 9, negative 3 labeled B, one leg is from negative 6, negative 2 to negative 6, negative 3, and the second leg is from negative 9, negative 3 to negative 6, negative 3.
Which statement about the slope of the line is true?
Group of answer choices
It is fraction 1 over 3 throughout the line.
It is 3 throughout the line.
The slope from point O to point A is three times the slope of the line from point A to point B.
The slope from point O to point A is fraction 1 over 3 time the slope of the line from point A to point B.
Flag question: Question 8
Question 82 pts
M08.B-E.2.1.3
Lesson 3
What is the initial value of the equation represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
Group of answer choices
0
5
2
1
Flag question: Question 9
Question 92 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 9 inches long and is melting at a rate of 0.6 inches per hour.
Find and interpret the slope for this relationship.
Group of answer choices
9; the length of the icicle when the student first measures it
0.6; for every additional hour, the length of the icicle increases by 0.6 inches
−9; the length of the icicle when the student first measures it
−0.6; for every additional hour, the length of the icicle decreases by 0.6 inches
Flag question: Question 10
Question 102 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A cab company charges a fixed amount plus a fee based on the distance traveled. The cost chart for the company is shown:
Cost Chart
Distance traveled (miles) (x)
Cost (dollars)
(y)
0
5
1
8
2
11
What is the fixed amount charged?
Group of answer choices
$3
$8
$9
$5
Flag question: Question 11
Question 112 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
Elena sells ice cream bars at the beach. In addition to a fixed salary, she earns a commission for each ice cream bar she sells. The table shows Elena's total earnings, y, from selling x bars of ice cream:
Ice Cream Sales and Earnings
Number of Bars Sold (x)
Total Earnings (dollars) (y)
0
30
1
33
2
36
3
39
Which equation best shows the relationship between x and y?
Group of answer choices
y = x + 36
y = 3x + 30
y = x + 30
y = 3x + 36
Flag question: Question 12
Question 122 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50
Which of the following graphs shows the relationship given in the table?
Group of answer choices
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
1 answer for each please, in the most simplest form
Group of answer choices
a graph of a line that passes through the points 0 comma 4 and 2 comma 0
a graph of a line that passes through the points 0 comma negative 3 and 1 comma negative 1
a graph of a line that passes through the points 0 comma 0 and 1 comma 6
a graph of a line that passes through the points 0 comma negative 1 and 2 comma negative 1
Flag question: Question 2
Question 22 pts
M08.B-E.2.1.1
Lesson 1
Which of the following tables represents a linear relationship that is also proportional?
Group of answer choices
x 3 1 −1
y −2 0 2
x 6 3 0
y −2 −1 0
x 0 1 2
y −1 0 1
x −4 −2 0
y 0 2 4
Flag question: Question 3
Question 32 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the distance, y, that a car traveled in x hours:
A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to 225 in increments of 45 for each grid line. A line is shown connecting ordered pairs 1, 45 and 2, 90 and 3, 135 and 4, 180. The title of the graph is Rate of Travel.
What is the rate of change (slope) for the relationship represented in the graph?
Group of answer choices
fraction 1 over 90
fraction 1 over 45
90
45
Flag question: Question 4
Question 42 pts
M08.B-E.2.1.3
Lesson 2
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x axis and Distance from Island in miles labeled on y axis. The scale on the x axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
What is the speed of the motorboat?
Group of answer choices
50 miles per hour
75 miles per hour
25 miles per hour
225 miles per hour
Flag question: Question 5
Question 52 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the number of paintballs a machine launches, y, in x seconds:
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line. A line is shown connecting points on ordered pair 2, 12 and 4, 24 and 6, 36 and 8, 48.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
Group of answer choices
fraction 2 over 12
fraction 12 over 2
fraction 2 over 48
fraction 48 over 2
Flag question: Question 6
Question 62 pts
M08.B-E.2.1.1
Lesson 2
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,240 and 4,320 and 5,400 and 6,480. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 450 in increments of 90 for each grid line. A line passing through the ordered pairs 2, 90 and 4, 180 and 6, 270 and 8, 360 is drawn.
Which statement correctly compares the rates (slopes) of these representations?
Group of answer choices
The rate of the table is greater than the rate of the graph.
The rates of the table and the graph are the same.
The rate of the graph is greater than the rate of the table.
Flag question: Question 7
Question 72 pts
M08.B-E.2.1.2
Lesson 3
The figure shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 15 to positive 15 in increments of 3 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 12, negative 4, and 0, 0, and 12, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to negative 6, negative 2 labeled A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 6, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 6, negative 2 to negative 9, negative 3 labeled B, one leg is from negative 6, negative 2 to negative 6, negative 3, and the second leg is from negative 9, negative 3 to negative 6, negative 3.
Which statement about the slope of the line is true?
Group of answer choices
It is fraction 1 over 3 throughout the line.
It is 3 throughout the line.
The slope from point O to point A is three times the slope of the line from point A to point B.
The slope from point O to point A is fraction 1 over 3 time the slope of the line from point A to point B.
Flag question: Question 8
Question 82 pts
M08.B-E.2.1.3
Lesson 3
What is the initial value of the equation represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
Group of answer choices
0
5
2
1
Flag question: Question 9
Question 92 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 9 inches long and is melting at a rate of 0.6 inches per hour.
Find and interpret the slope for this relationship.
Group of answer choices
9; the length of the icicle when the student first measures it
0.6; for every additional hour, the length of the icicle increases by 0.6 inches
−9; the length of the icicle when the student first measures it
−0.6; for every additional hour, the length of the icicle decreases by 0.6 inches
Flag question: Question 10
Question 102 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A cab company charges a fixed amount plus a fee based on the distance traveled. The cost chart for the company is shown:
Cost Chart
Distance traveled (miles) (x)
Cost (dollars)
(y)
0
5
1
8
2
11
What is the fixed amount charged?
Group of answer choices
$3
$8
$9
$5
Flag question: Question 11
Question 112 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
Elena sells ice cream bars at the beach. In addition to a fixed salary, she earns a commission for each ice cream bar she sells. The table shows Elena's total earnings, y, from selling x bars of ice cream:
Ice Cream Sales and Earnings
Number of Bars Sold (x)
Total Earnings (dollars) (y)
0
30
1
33
2
36
3
39
Which equation best shows the relationship between x and y?
Group of answer choices
y = x + 36
y = 3x + 30
y = x + 30
y = 3x + 36
Flag question: Question 12
Question 122 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50
Which of the following graphs shows the relationship given in the table?
Group of answer choices
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
1 answer for each please, in the most simplest form
Answers
Answered by
GPT-4o mini
Here are the answers for each question in the simplest form:
**Question 1:**
**Answer:** a graph of a line that passes through the points (0, 0) and (1, 6)
*(This graph represents a proportional relationship because it passes through the origin.)*
**Question 2:**
**Answer:**
x: 0, 1, 2
y: -1, 0, 1
*(This table represents a proportional relationship since it goes through (0,0) when adjusted for proportion.)*
**Question 3:**
**Answer:** 45
*(The slope can be calculated as change in distance (y) over change in time (x), which here is 180/4 = 45.)*
**Question 4:**
**Answer:** 50 miles per hour
*(The speed can be found from the slope: increase in distance over increase in time. The line shows that the distance increases by 50 for every hour.)*
**Question 5:**
**Answer:** \(\frac{12}{2}\)
*(This gives the rate of launch per second.)*
**Question 6:**
**Answer:** The rates of the table and the graph are the same.
*(Both relationships have the same slope based on respective increments.)*
**Question 7:**
**Answer:** The slope from point O to point A is three times the slope of the line from point A to point B.
*(This indicates a change in steepness, as per the description of triangles sampled.)*
**Question 8:**
**Answer:** 2
*(The initial value is represented by the y-intercept of the line at (0, 2).)*
**Question 9:**
**Answer:** -0.6; for every additional hour, the length of the icicle decreases by 0.6 inches
*(This represents the rate at which the icicle is melting.)*
**Question 10:**
**Answer:** $5
*(This is the initial cost charge when no distance is traveled.)*
**Question 11:**
**Answer:** y = 3x + 30
*(The number of bars sold correlates linuearly with the earnings starting at $30.)*
**Question 12:**
**Answer:** graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point (0, 5.5) through the point (5, 13)
*(This reflects the relationship accurately based on the data provided.)*
**Question 1:**
**Answer:** a graph of a line that passes through the points (0, 0) and (1, 6)
*(This graph represents a proportional relationship because it passes through the origin.)*
**Question 2:**
**Answer:**
x: 0, 1, 2
y: -1, 0, 1
*(This table represents a proportional relationship since it goes through (0,0) when adjusted for proportion.)*
**Question 3:**
**Answer:** 45
*(The slope can be calculated as change in distance (y) over change in time (x), which here is 180/4 = 45.)*
**Question 4:**
**Answer:** 50 miles per hour
*(The speed can be found from the slope: increase in distance over increase in time. The line shows that the distance increases by 50 for every hour.)*
**Question 5:**
**Answer:** \(\frac{12}{2}\)
*(This gives the rate of launch per second.)*
**Question 6:**
**Answer:** The rates of the table and the graph are the same.
*(Both relationships have the same slope based on respective increments.)*
**Question 7:**
**Answer:** The slope from point O to point A is three times the slope of the line from point A to point B.
*(This indicates a change in steepness, as per the description of triangles sampled.)*
**Question 8:**
**Answer:** 2
*(The initial value is represented by the y-intercept of the line at (0, 2).)*
**Question 9:**
**Answer:** -0.6; for every additional hour, the length of the icicle decreases by 0.6 inches
*(This represents the rate at which the icicle is melting.)*
**Question 10:**
**Answer:** $5
*(This is the initial cost charge when no distance is traveled.)*
**Question 11:**
**Answer:** y = 3x + 30
*(The number of bars sold correlates linuearly with the earnings starting at $30.)*
**Question 12:**
**Answer:** graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point (0, 5.5) through the point (5, 13)
*(This reflects the relationship accurately based on the data provided.)*