To predict how much Amanda will make if she babysits for 10 hours, we can find the equation of the line that passes through the points (5, 0) and (15, 1) and then use that equation to calculate the amount for 10 hours.
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Find the slope (m) of the line: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{15 - 5} = \frac{1}{10} \]
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Use the point-slope form of the equation of a line: The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] We can use the point (5, 0): \[ y - 0 = \frac{1}{10}(x - 5) \] Simplifying this, we get: \[ y = \frac{1}{10}(x - 5) = \frac{1}{10}x - \frac{1}{2} \]
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Calculate the amount for 10 hours: Substitute \(x = 10\) into the equation: \[ y = \frac{1}{10}(10) - \frac{1}{2} = 1 - 0.5 = 0.5 \]
Therefore, if Amanda babysits for 10 hours, she will make $0.50.
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