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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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Answer 1

The relationship between quantity and cost in the graph is proportional, which means it can be expressed in the form of the equation \( y = kx \), where \( y \) is the cost, \( x \) is the quantity, and \( k \) is the constant of proportionality (or the price per item).

From the points plotted on the graph, we can see that:

• When \( x = 1 \), \( y = 9 \)
• When \( x = 2 \), \( y = 18 \)
• When \( x = 3 \), \( y = 27 \)
• When \( x = 4 \), \( y = 36 \)

To find \( k \), we can use any of these points. Using the first point:

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

So, the equation of the proportional relationship is:

\[ y = 9x \]

Thus, the derived equation for the relationship in the graph is \( y = 9x \).