Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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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.
To find the equation of the line y=mx through the origin, we need to determine the slope of the line.
The slope (m) can be calculated using the formula: m = (change in y) / (change in x)
In this case, the change in y is 8 - 4 = 4 and the change in x is 2 - 1 = 1.
So, the slope (m) is 4/1 = 4.
Therefore, the equation of the line y=mx through the origin is 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)
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To find the equation of the proportional relationship through the origin, we can use the slope-intercept form of a linear equation, which is y = mx.
First, let's find the slope (m). The slope is equal to the change in y divided by the change in x.
From the graph, we can see that as the quantity increases by 1 (change in x), the cost increases by 9 (change in y). So, the slope is 9/1 = 9.
Now that we have the slope, we can write the equation of the line as y = 9x. This equation represents the proportional relationship between the quantity of footballs and their cost, as shown in the graph.
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)
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To find the equation of the line y=mx through the origin, we need to determine the slope of the line.
The slope (m) can be calculated using the formula: m = (change in y) / (change in x)
In this case, the change in y is 3 - 1 = 2 and the change in x is 9 - 3 = 6.
So, the slope (m) is 2/6 = 1/3.
Therefore, the equation of the line y=mx through the origin is 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,
)
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To find the y-coordinate of the ordered pairs for the equation y=14x, we can substitute the given values of x into the equation and solve for y.
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)