Question

1. mike earned the amounts listed in the table below.

hours worked (h)	earned (e)
25	$287.50
40	$460

which equation could be used to find the amount of money mike earns, e, for any number of hours worked, h?

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Explanation:

Step1: Find the rate of pay (slope)

To find the equation relating hours worked (\(h\)) and earnings (\(E\)), we first determine the rate of pay (slope \(m\)) using the formula \(m=\frac{E_2 - E_1}{h_2 - h_1}\). Using the first two points \((12, 138)\) and \((25, 287.50)\):
\(m=\frac{287.50 - 138}{25 - 12}=\frac{149.50}{13}=11.5\).

Step2: Verify the rate with another point

Check with \((40, 460)\): \(11.5\times40 = 460\), which matches. So the relationship is linear, and the equation is \(E = 11.5h\) (since there is no y - intercept, as \(h = 0\) would mean \(E = 0\)).

Answer:

\(E = 11.5h\) (or \(E=\frac{23}{2}h\))