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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The equation of the proportional relationship through the origin can be derived by finding the slope of the line segment connecting the points (0,0) and (4,36).
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (0,0) and (4,36):
slope = (36 - 0) / (4 - 0)
= 36 / 4
= 9
Since the proportional relationship goes through the origin, the equation can be written as:
y = mx
where m is the slope.
Therefore, the equation of the proportional relationship through the origin is:
y = 9x
To derive the equation of the proportional relationship through the origin, we need to determine the slope of the line segment connecting the points on the graph.
The slope of a line can be calculated using the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
Let's calculate the slope using two points on the line segment. Let's take the points (0,0) and (1,9):
slope = (9 - 0) / (1 - 0)
= 9 / 1
= 9
So, the slope of the line segment is 9.
The equation of a proportional relationship is in the form:
y = mx
where m is the slope. Since we are looking for a relationship through the origin (0,0), the y-intercept is 0.
Therefore, the equation of the proportional relationship through the origin is:
y = 9x