To derive the equation of the proportional relationship through the origin, we need to find the slope of the line represented by the graph.
Looking at the graph, we can see that the price (P) is on the y-axis and the number of footballs (N) is on the x-axis. The line passes through the origin, indicating that the relationship is proportional.
The slope of the line represents the rate of change of the price with respect to the number of footballs. In other words, it tells us how much the price changes for each additional football.
To find the slope, we can choose two points on the line and calculate the rise over run.
Let's choose the points (0, 0) and (4, 32) from the graph.
Rise = Change in y-values = 32 - 0 = 32
Run = Change in x-values = 4 - 0 = 4
Slope = Rise/Run = 32/4 = 8
Therefore, the slope of the line is 8.
Since the relationship is proportional and passes through the origin, the equation of the line can be written as:
P = kN
Where P represents the price, N represents the number of footballs, and k is the constant of proportionality.
From the slope, we know that k = 8.
Hence, the equation of the proportional relationship through the origin is:
P = 8N
The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
1 answer