Use the image to answer the question

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 shown in the graph, we can observe the plotted points. They are at the coordinates:

• (0, 0)
• (1, 9)
• (2, 18)
• (3, 27)
• (4, 36)

To find the equation of the line, we can identify the relationship between the quantity (x) and the cost (y).

The pattern indicates that for each increase of 1 in quantity, the cost increases by 9. This suggests a constant rate of change (slope) of 9.

The relationship can be expressed as:

\[ y = kx \]

where \( k \) is the constant of proportionality (the slope). In this case, \( k = 9 \).

Thus, the equation of the proportional relationship through the origin is:

\[ y = 9x \]