the variable y has a proportional relationship with x as suggested by the graph. use the graph to find the…

Explanation:

Step1: Recall the proportional relationship formula

For a proportional relationship, the formula is ( y = kx ), where ( k ) is the constant of proportionality. This can be rewritten as ( k=\frac{y}{x} ).

Step2: Identify a point from the graph

Looking at the graph, we can assume a point (let's say when ( x = 10 ), ( y = 150 )) (we need to check the grid, but typically in such problems, we pick a point where ( x ) and ( y ) are clear. Let's confirm: if the graph passes through (10,150), then we use this point.

Step3: Calculate the constant of proportionality

Using ( k=\frac{y}{x} ), substitute ( x = 10 ) and ( y = 150 ). So ( k=\frac{150}{10}=15 ). Wait, maybe another point. Wait, maybe the graph has a point like (20, 300)? Let's check: ( \frac{300}{20}=15 ). Or (5,75): ( \frac{75}{5}=15 ). So the constant of proportionality ( k ) is 15. Wait, maybe I misread the graph. Wait, let's see the y-axis and x-axis. Suppose the x-axis is in units, and y-axis too. Let's take a clear point. Let's say when x=10, y=150. Then ( k = y/x = 150/10 = 15 ). So the constant of proportionality is 15.

Wait, maybe the graph is such that when x=2, y=30? No, maybe the grid is with x and y. Let's re-express. The formula for constant of proportionality in a proportional relationship (linear through origin) is slope, which is ( k = \frac{y}{x} ). So we need to pick a point (x,y) on the line. Let's assume from the graph, a point is (10, 150) (since the grid lines: let's say each x grid is 10, y grid is 150? No, maybe x=10, y=150. Then ( k = 150/10 = 15 ). So the constant of proportionality is 15.

Answer:

15