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 find the slope of the line passing through the origin and the data points on the graph.
The graph shows the price of footballs on the y-axis and the quantity of footballs on the x-axis. Since the relationship is proportional, we expect a straight line passing through the origin (0,0).
Let's take two points on the graph that lie on this line: (10, 20) and (5, 10).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the equation: slope = (y2 - y1) / (x2 - x1).
Using our two points, the slope of the line passing through them is: slope = (10 - 0) / (5 - 0) = 10 / 5 = 2.
Therefore, the equation of the proportional relationship through the origin is: y = 2x.
In this case, y represents the price of footballs, and x represents the quantity of footballs.