Question

Graphing Proportional Relationships Practice
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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)

Answer 1

To derive the equation of the proportional relationship represented in the graph, we need to identify the relationship between the quantities on the horizontal axis (Quantity of footballs) and the values on the vertical axis (Cost).

From the points given in the graph:
- At 0 footballs, the cost is $0.
- At 1 football, the cost is $9.
- At 2 footballs, the cost is $18.
- At 3 footballs, the cost is $27.
- At 4 footballs, the cost is $36.

This indicates that the cost increases consistently as the quantity of footballs increases. To find the equation, we can determine the constant of proportionality (k) by using one of the points.

Using the point (1, 9):
- Quantity (x) = 1
- Cost (y) = 9

To find k:
\[
k = \frac{y}{x} = \frac{9}{1} = 9
\]

Thus, the equation representing the proportional relationship is:
\[
y = kx
\]
Substituting k:
\[
y = 9x
\]

So the equation of the proportional relationship through the origin is:
\[
\text{Cost} = 9 \times \text{Quantity}
\]
Or,
\[
C = 9Q
\]
where C is the cost and Q is the quantity of footballs.