b=10
b equals 10
Determine the initial value in the following description. A surfboard rental service charges $10 to reserve a board, and $5 for each hour of rental. (1 point)
Responses
b=10
b equals 10
b=−10
b equals negative 10
b=−5
b equals negative 5
b=5
23 answers
Use the table to answer the question.
x
y
−5
8
−7
14
Determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
Responses
m=−3, b=−7
m equals negative 3 comma b equals negative 7
m=−0.5, b=10.5
m equals negative 0.5 comma b equals 10.5
m=−0.5, b=5.5
m equals negative 0.5 comma b equals 5.5
m=−7, b=−3
x
y
−5
8
−7
14
Determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
Responses
m=−3, b=−7
m equals negative 3 comma b equals negative 7
m=−0.5, b=10.5
m equals negative 0.5 comma b equals 10.5
m=−0.5, b=5.5
m equals negative 0.5 comma b equals 5.5
m=−7, b=−3
m=-3, b=8
m equals negative 3, b equals 8
m equals negative 3, b equals 8
Use the table to answer the question.
Time spent driving (hours) Distance traveled (miles)
0 0
1/2
30
1 1/2
90
2 120
4 240
The table shows the distance traveled on a bus trip from Houston, TX to Dallas, TX as a function of time. Find the rate at which the bus is traveling.
(1 point)
Responses
70 mph
70 mph
55 mph
55 mph
60 mph
60 mph
65 mph
65 mph
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Time spent driving (hours) Distance traveled (miles)
0 0
1/2
30
1 1/2
90
2 120
4 240
The table shows the distance traveled on a bus trip from Houston, TX to Dallas, TX as a function of time. Find the rate at which the bus is traveling.
(1 point)
Responses
70 mph
70 mph
55 mph
55 mph
60 mph
60 mph
65 mph
65 mph
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To find the rate at which the bus is traveling, we need to find the speed which is the rate of distance change with respect to time.
Distance traveled from Houston to Dallas is 240 miles.
Time taken to travel from Houston to Dallas is 4 hours.
So, speed = distance / time
speed = 240 miles / 4 hours
speed = 60 mph
Therefore, the bus is traveling at a rate of 60 mph.
So, the correct response is:
60 mph
Distance traveled from Houston to Dallas is 240 miles.
Time taken to travel from Houston to Dallas is 4 hours.
So, speed = distance / time
speed = 240 miles / 4 hours
speed = 60 mph
Therefore, the bus is traveling at a rate of 60 mph.
So, the correct response is:
60 mph
Which two points on a linear graph showing time and distance would indicate a rate of change of 80 km per hour?(1 point)
Responses
(4,400)
and (6,480)
left parenthesis 4 comma 400 right parenthesis and left parenthesis 6 comma 480 right parenthesis
(5,400)
and (6,560)
left parenthesis 5 comma 400 right parenthesis and left parenthesis 6 comma 560 right parenthesis
(4,320)
and (6,480)
left parenthesis 4 comma 320 right parenthesis and left parenthesis 6 comma 480 right parenthesis
(4,480)
and (6,600)
left parenthesis 4 comma 480 right parenthesis and left parenthesis 6 comma 600 right parenthesis
Responses
(4,400)
and (6,480)
left parenthesis 4 comma 400 right parenthesis and left parenthesis 6 comma 480 right parenthesis
(5,400)
and (6,560)
left parenthesis 5 comma 400 right parenthesis and left parenthesis 6 comma 560 right parenthesis
(4,320)
and (6,480)
left parenthesis 4 comma 320 right parenthesis and left parenthesis 6 comma 480 right parenthesis
(4,480)
and (6,600)
left parenthesis 4 comma 480 right parenthesis and left parenthesis 6 comma 600 right parenthesis
To determine the points on the linear graph indicating a rate of change of 80 km per hour, we need to look for two points where the change in distance divided by the change in time gives us a rate of 80 km per hour.
Let's calculate the rate of change for each pair of points:
For (4,400) and (6,480):
Rate of change = (480 - 400) / (6 - 4) = 80 / 2 = 40 km per hour
For (5,400) and (6,560):
Rate of change = (560 - 400) / (6 - 5) = 160 / 1 = 160 km per hour
For (4,320) and (6,480):
Rate of change = (480 - 320) / (6 - 4) = 160 / 2 = 80 km per hour
For (4,480) and (6,600):
Rate of change = (600 - 480) / (6 - 4) = 120 / 2 = 60 km per hour
The pair of points (4,320) and (6,480) give a rate of change of 80 km per hour.
Therefore, the answer is:
(4,320) and (6,480)
Let's calculate the rate of change for each pair of points:
For (4,400) and (6,480):
Rate of change = (480 - 400) / (6 - 4) = 80 / 2 = 40 km per hour
For (5,400) and (6,560):
Rate of change = (560 - 400) / (6 - 5) = 160 / 1 = 160 km per hour
For (4,320) and (6,480):
Rate of change = (480 - 320) / (6 - 4) = 160 / 2 = 80 km per hour
For (4,480) and (6,600):
Rate of change = (600 - 480) / (6 - 4) = 120 / 2 = 60 km per hour
The pair of points (4,320) and (6,480) give a rate of change of 80 km per hour.
Therefore, the answer is:
(4,320) and (6,480)
In a linear function that describes a real-world situation, what part of the function corresponds to the initial value?(1 point)
Responses
the x
-value when y=1
the x -value when y equals 1
the y
-intercept
the y -intercept
the y
-value when x=1
the y -value when x equals 1
the x
-intercept
Responses
the x
-value when y=1
the x -value when y equals 1
the y
-intercept
the y -intercept
the y
-value when x=1
the y -value when x equals 1
the x
-intercept
The y-intercept corresponds to the initial value in a linear function that describes a real-world situation.
So, the correct response is:
the y-intercept
So, the correct response is:
the y-intercept
You are taking a road trip across several states. Your distance from your final destination is modeled with the equation f(x)=−350x+1,400
, where x
represents the number of days you have been traveling. Identify and interpret the initial value.(1 point)
Responses
The initial value of 350 represents the distance from your starting point to your final destination.
The initial value of 350 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance you travel each day.
The initial value of 1,400 represents the distance you travel each day.
The initial value of 350 represents the distance you travel each day.
, where x
represents the number of days you have been traveling. Identify and interpret the initial value.(1 point)
Responses
The initial value of 350 represents the distance from your starting point to your final destination.
The initial value of 350 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance from your starting point to your final destination.
The initial value of 1,400 represents the distance you travel each day.
The initial value of 1,400 represents the distance you travel each day.
The initial value of 350 represents the distance you travel each day.
The initial value in the given equation is 1,400. This value represents the distance from your starting point to your final destination.
So, the correct response is:
The initial value of 1,400 represents the distance from your starting point to your final destination.
So, the correct response is:
The initial value of 1,400 represents the distance from your starting point to your final destination.
What does the graph of a linear function look like?(1 point)
Responses
a circle
a circle
a parabola
a parabola
a straight line
a straight line
a curvy line
Responses
a circle
a circle
a parabola
a parabola
a straight line
a straight line
a curvy line
a straight line
Marie orders a shuttle to the airport and learns that it will cost $15 plus $0.50 per mile. Write the equation of a linear function that models the relationship between number of miles and total cost of the shuttle.(1 point)
Responses
y=7.5x
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 7.5 x , where x is the number of miles and y is the total cost of the shuttle.
y=0.5x+15
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 0.5 x plus 15 , where x is the number of miles and y is the total cost of the shuttle.
y=15x+0.5
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 15 x plus 0.5 , where x is the number of miles and y is the total cost of the shuttle.
y=x+7.5
, where x
is the number of miles and y
is the total cost of the shuttle.
Responses
y=7.5x
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 7.5 x , where x is the number of miles and y is the total cost of the shuttle.
y=0.5x+15
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 0.5 x plus 15 , where x is the number of miles and y is the total cost of the shuttle.
y=15x+0.5
, where x
is the number of miles and y
is the total cost of the shuttle.
y equals 15 x plus 0.5 , where x is the number of miles and y is the total cost of the shuttle.
y=x+7.5
, where x
is the number of miles and y
is the total cost of the shuttle.
y=0.5x+15, where x is the number of miles and y is the total cost of the shuttle.
se the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 50 to 50 in ten unit increments. The y-axis ranges from negative 20 to 120 in ten unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis 10 comma 70 right parenthesis and left parenthesis 25 comma 100 right parenthesis.
Write the equation of the linear function shown on the graph.
(1 point)
Responses
y=1/2x+50
y equals Start Fraction 1 over 2 End Fraction x plus 50
y=1/2x−25
y equals Start Fraction 1 over 2 End Fraction x minus 25
y=2x+50
y equals 2 x plus 50
y=2x−25
y equals 2 x minus 25
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An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 50 to 50 in ten unit increments. The y-axis ranges from negative 20 to 120 in ten unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis 10 comma 70 right parenthesis and left parenthesis 25 comma 100 right parenthesis.
Write the equation of the linear function shown on the graph.
(1 point)
Responses
y=1/2x+50
y equals Start Fraction 1 over 2 End Fraction x plus 50
y=1/2x−25
y equals Start Fraction 1 over 2 End Fraction x minus 25
y=2x+50
y equals 2 x plus 50
y=2x−25
y equals 2 x minus 25
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By using the two points (10,70) and (25,100) that the line passes through:
First, find the slope:
slope (m) = (y2 - y1) / (x2 - x1)
slope (m) = (100 - 70) / (25 - 10) = 30 / 15 = 2
Then, use the slope to find the y-intercept (b) by substituting one of the points:
y = mx + b
100 = 2(25) + b
100 = 50 + b
b = 50
Therefore, the equation of the linear function shown on the graph is: y = 2x + 50.
So, the correct response is:
y = 2x + 50
First, find the slope:
slope (m) = (y2 - y1) / (x2 - x1)
slope (m) = (100 - 70) / (25 - 10) = 30 / 15 = 2
Then, use the slope to find the y-intercept (b) by substituting one of the points:
y = mx + b
100 = 2(25) + b
100 = 50 + b
b = 50
Therefore, the equation of the linear function shown on the graph is: y = 2x + 50.
So, the correct response is:
y = 2x + 50
Use the image to answer the question.
Linear Function 1:
A coordinate plane shows the x-axis ranging from negative 1 to 4 in increments of 1 and the y-axis ranging from negative 1 to 13 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 1 comma 9 right parenthesis and left parenthesis 2 comma 12 right parenthesis.
Linear Function 2:
x
y
0 2
5 42
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?
(1 point)
Responses
Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
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Linear Function 1:
A coordinate plane shows the x-axis ranging from negative 1 to 4 in increments of 1 and the y-axis ranging from negative 1 to 13 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 1 comma 9 right parenthesis and left parenthesis 2 comma 12 right parenthesis.
Linear Function 2:
x
y
0 2
5 42
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?
(1 point)
Responses
Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
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To compare the rate of change between Linear Function 1 and Linear Function 2, we need to find the slope of each function.
Linear Function 1 with points (1,9) and (2,12):
Rate of change = (y2 - y1) / (x2 - x1) = (12 - 9) / (2 - 1) = 3 / 1 = 3
Linear Function 2 with points (0,2) and (5,42):
Rate of change = (y2 - y1) / (x2 - x1) = (42 - 2) / (5 - 0) = 40 / 5 = 8
Therefore, Linear Function 2 has the greater rate of change with a rate of change equal to 8, while Linear Function 1 has a rate of change equal to 3.
So, the correct response is:
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 1 with points (1,9) and (2,12):
Rate of change = (y2 - y1) / (x2 - x1) = (12 - 9) / (2 - 1) = 3 / 1 = 3
Linear Function 2 with points (0,2) and (5,42):
Rate of change = (y2 - y1) / (x2 - x1) = (42 - 2) / (5 - 0) = 40 / 5 = 8
Therefore, Linear Function 2 has the greater rate of change with a rate of change equal to 8, while Linear Function 1 has a rate of change equal to 3.
So, the correct response is:
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
A bathtub is filled with 40 gallons of water. The water starts draining out of the tub at a rate of 8 gallons per minute. Choose the sketch of a graph that shows the relationship between the number of minutes since the tub started draining and the number of gallons of water in the tub.(1 point)
Responses
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
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Responses
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.
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The relationship described is that the water in the tub is drained out at a constant rate. This means that the amount of water in the tub reduces at a constant pace, making the relationship linear.
Therefore, the sketch of the graph that shows the relationship between the number of minutes since the tub started draining and the number of gallons of water in the tub should be a straight line.
The correct response is:
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: (5, 0) and (0, 40).
Therefore, the sketch of the graph that shows the relationship between the number of minutes since the tub started draining and the number of gallons of water in the tub should be a straight line.
The correct response is:
A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: (5, 0) and (0, 40).
wow good job bot you actually all the questions right
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