Question

the graph represents the direct variation function between earnings in dollars and hours worked. store clerk pay which equation can be used to describe the direct variation function between e, the total earnings in dollars, and h, the number of hours worked? e = 1.5h e = 7.5h e = 13h e = 15h

Explanation:

Step1: Recall direct variation formula

The formula for direct variation is \( E = kh \), where \( k \) is the constant of variation (rate of pay per hour).

Step2: Find a point on the graph

From the graph, when \( h = 12 \) (assuming the x - axis grid, let's check the point where earnings are 90. If we assume when \( h = 12 \), \( E = 90 \) (since from the graph, the line passes near \( h = 12 \), \( E = 90 \)). Then \( k=\frac{E}{h}=\frac{90}{12} = 7.5 \). So the equation is \( E = 7.5h \). We can also check with other points. For example, if \( h = 10 \), \( E=7.5\times10 = 75 \), which matches the graph's trend (the line at \( h = 10 \) should be around 75, which is consistent).

Answer:

\( E = 7.5h \) (the option with \( E = 7.5h \))