3. Use the graph to answer the questions.
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. The constant of proportionality is
b. Write an equation that represents the linear graph.
c. This is a proportional relationship because the graph shows
a. The constant of proportionality is the slope of the line, which is $\frac{1}{2}$.
b. An equation that represents the linear graph is $y = \frac{1}{2}x$.
c. This is a proportional relationship because the graph shows a straight line passing through the origin.
1. Given the table for x, tickets sold and y, money earned:
x - tickets 4 9 8 5 7
y - $ earned 48 108 96 60 84
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. Every ticket sold is dollars earned.
b. Dollars/1 ticket is called a .
c. This relationship is , because 0 tickets sold is dollars earned.
Question 2
2. Given the table for x, time in minutes and y, distance traveled:
x - time 4 3 10 7 9
y - distance 76 57 190 133 171
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. Every minute meters are traveled.
b. Write an equation to show the relationship between x and y.
c. This relationship is because the y-intercept is .
Question 3
3. Use the graph to answer the questions.
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. The constant of proportionality is
b. Write an equation that represents the linear graph.
c. This is a proportional relationship because the graph shows .
Question 4
4. Solve this equation for y: y3=2x
(1 point)
Responses
y=2x−3
y is equal to 2 x minus 3
y=6x
y is equal to 6 x
y=2x+3
y is equal to 2 x plus 3
y=23x
y is equal to 2 thirds x
Question 5
5. Over the summer, you text a bunch. Let’s say you make 50 texts every 2 days.
The graph represents the scenario.
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Fill in the missing parts of the table:
x - # of days 0 a. 7 b.
y - # of texts c. 75 d. 300
a.
b. Response area
c.
d.
Question 1:
a. Every ticket sold is $12 earned.
b. Dollars/1 ticket is called a unit rate.
c. This relationship is linear, because 0 tickets sold is 0 dollars earned.
Question 2:
a. Every minute 19 meters are traveled.
b. An equation to show the relationship between x and y is y = 19x.
c. This relationship is linear, because the y-intercept is 0.
Question 3:
a. The constant of proportionality is the slope of the line, which cannot be determined from the information given.
b. An equation that represents the linear graph cannot be determined without the y-intercept.
c. This is a proportional relationship because the graph shows a straight line passing through the origin.
Question 4:
The correct response is: y = 2x³
Question 5:
a. 0
b. 140
c. 0
d. 700
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
To find the equation of the line y=mx through the origin, we need to find the slope (m) of the line.
Using the points (1,4) and (2,8), we can calculate the slope:
m = (change in y) / (change in x) = (8 - 4) / (2 - 1) = 4 / 1 = 4.
Now that we have the slope (m), we can write the equation of the line y=mx through the origin:
y = 4x.
Use the image to answer the question.
An illustration shows a graph labeled Football Cost. The horizontal axis is labeled Quantity and ranges from 0 to 5 in increments of 1. The vertical axis is labeled Cost and ranges from 0 to 39 in increments of 3. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 18 right parenthesis, left parenthesis 3 comma 27 right parenthesis, and left parenthesis 4 comma 36 right parenthesis.
The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
(1 point)
To derive the equation of the proportional relationship through the origin, we need to find the slope (m) of the line segment.
Using the points (0,0) and (4,36), we can calculate the slope:
m = (change in y) / (change in x) = (36 - 0) / (4 - 0) = 36 / 4 = 9.
Now that we have the slope (m), we can write the equation of the line through the origin:
y = 9x.
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
To write the equation of the line y=mx through the origin, we need to find the slope (m) of the line.
Using the points (3,1) and (9,3), we can calculate the slope:
m = (change in y) / (change in x) = (3 - 1) / (9 - 3) = 2 / 6 = 1/3.
Now that we have the slope (m), we can write the equation of the line y=mx through the origin:
y = (1/3)x.
Use the table to answer the question.
x y (x, y)
0 (0, )
4 (4, )
8 (8, )
Complete the ordered pairs in the table by finding the y-coordinate of the ordered pairs for the equation y=14x.
(2 points)
x y (x, y)
0 (0,
)
4 (4,
)
8 (8,
)