The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin
To derive the equation of the proportional relationship through the origin, we need to determine the slope of the graph.
Let's take two points from the graph: (3, 15) and (6, 30).
The formula for calculating the slope between two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
Using the points (3, 15) and (6, 30), we can substitute into the formula:
slope = (30 - 15) / (6 - 3)
slope = 15 / 3
slope = 5
Since the proportional relationship goes through the origin, the y-intercept is 0.
Therefore, the equation of the proportional relationship through the origin is:
y = 5x