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.
The slope of a line can be found using the formula:
m = (change in y) / (change in x)
In this case, the line passes through the points (1,4) and (2,8). The change in y is 8 - 4 = 4 and the change in x is 2 - 1 = 1.
So, the slope is m = 4 / 1 = 4.
Therefore, the equation of the line y=mx through the origin is y = 4x.
To find the equation of the line y=mx through the origin, we need to find the slope (m) of the line.
The slope of a line can be found using the formula:
m = (change in y) / (change in x)
In this case, the line passes through the points (3,1) and (9,3). The change in y is 3 - 1 = 2 and the change in x is 9 - 3 = 6.
So, the slope is m = 2 / 6 = 1/3.
Therefore, the equation of the line y=mx through the origin is y = (1/3)x.
To find the equation of the proportional relationship through the origin, we need to find the slope (m) of the line.
The slope of a line can be found using the formula:
m = (change in y) / (change in x)
In this case, the line passes through the points (0,0) and (1,9). The change in y is 9 - 0 = 9 and the change in x is 1 - 0 = 1.
So, the slope is m = 9 / 1 = 9.
Therefore, the equation of the proportional relationship through the origin is y = 9x.
Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
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)
Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
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)
Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
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)
Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
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,
)
Use the image to answer the question.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 1 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
Use the graph of y=x to determine an additional ordered pair (x, y) that satisfies the equation. Find the ordered pair (x, y) if the x-coordinate is 3.
(1 point)
(3,
)
To find the y-coordinate for the ordered pair (3, y) on the line y = x, we can simply substitute x = 3 into the equation.
Therefore, when x = 3, y = 3.
So, the ordered pair is (3, 3).
Graphing Proportional Relationships Quick Check
1 of 51 of 5 Items
Question
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 line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=8x
y equals 8 x
y=3x
y equals 3 x
y=x
y equals x
y=33x
To find the equation of the line through the origin, we need to find the slope of the line.
The slope (m) can be found using the formula:
m = (change in y) / (change in x)
In this case, the line passes through the points (3,3) and (8,8). The change in y is 8 - 3 = 5 and the change in x is 8 - 3 = 5.
So, the slope is m = 5 / 5 = 1.
Therefore, the equation of the line through the origin is y = x.
Use the image to answer the question.
An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
(1 point)
Responses
y=36x
y equals 36 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=2x
y equals 2 x
y=12x
To find the equation of the line through the origin, we need to find the slope of the line.
The slope (m) can be found using the formula:
m = (change in y) / (change in x)
In this case, the line passes through the points (0,0) and (3,36). The change in y is 36 - 0 = 36 and the change in x is 3 - 0 = 3.
So, the slope is m = 36 / 3 = 12.
Therefore, the equation of the line through the origin is y = 12x.
Graphing Proportional Relationships Quick Check
3 of 53 of 5 Items
Question
Use the table to answer the question.
x y (x, y)
0 (0, )
1 (1, )
2 (2, )
Complete the ordered pairs in the table by finding the y-value of the ordered pairs for the equation y=5x.
(1 point)
Responses
(0, 0), (1, 5), (3, 15)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 3 comma 15 right parenthesis
(0, 0), (5, 1), (10, 2)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 5 comma 1 right parenthesis , left parenthesis 10 comma 2 right parenthesis
(0, 0), (1, 5), (2, 10)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 2 comma 10 right parenthesis
(0, 0), (1, 15) , (2, 25)
To find the y-values for the ordered pairs in the table, we substitute the corresponding x-values into the equation y=5x.
For x = 0, y = 5(0) = 0, so the ordered pair is (0,0).
For x = 1, y = 5(1) = 5, so the ordered pair is (1,5).
For x = 2, y = 5(2) = 10, so the ordered pair is (2,10).
Therefore, the completed table is:
x y (x, y)
0 0 (0,0)
1 5 (1,5)
2 10 (2,10)
Graph the proportional relationship y=−2x by plotting points.(1 point)
Responses
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.
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The correct response is:
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both ends joins three plotted points and extends beyond. The coordinates of the plotted points are: (0, 0), (1, -2), and (2, -4).
Graphing Proportional Relationships Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x?
(1 point)
Responses
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
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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 Response area dollars earned.
b. Dollars/1 ticket is called a Response area .
c. This relationship is Response area, because 0 tickets sold is Response area dollars earned
a. Every ticket sold is 12 dollars earned.
b. Dollars/1 ticket is called a unit rate.
c. This relationship is linear because for every increase of 1 ticket sold, there is a consistent increase of 12 dollars earned.
d. 0 tickets sold is 0 dollars earned.
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 Response area meters are traveled.
b. Write an equation to show the relationship between x and y. Response area
c. This relationship is Response area because the y-intercept is Response area .
thanks checking my work byeee
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
The equation of the line y=mx through the origin is y=mx.
To complete the table, we need to find the y-coordinate of each ordered pair for the equation y=14x.
For x = 0, y = 14(0) = 0, so the ordered pair is (0,0).
For x = 4, y = 14(4) = 56, so the ordered pair is (4,56).
For x = 8, y = 14(8) = 112, so the ordered pair is (8,112).
Therefore, the completed table is:
x y (x, y)
0 0 (0,0)
4 56 (4,56)
8 112 (8,112)