To analyze the situation and plot points on the linear function described by the equation \( C = 1.25m + 25 \), we can substitute different values of \( m \) (the miles driven) into the equation to find the corresponding values of \( C \) (the total cost).
Here are a few examples:
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If \( m = 0 \) (no miles driven): \[ C = 1.25(0) + 25 = 25 \] Point: (0, 25)
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If \( m = 10 \) (10 miles driven): \[ C = 1.25(10) + 25 = 12.5 + 25 = 37.5 \] Point: (10, 37.5)
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If \( m = 20 \) (20 miles driven): \[ C = 1.25(20) + 25 = 25 + 25 = 50 \] Point: (20, 50)
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If \( m = 50 \) (50 miles driven): \[ C = 1.25(50) + 25 = 62.5 + 25 = 87.5 \] Point: (50, 87.5)
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If \( m = 100 \) (100 miles driven): \[ C = 1.25(100) + 25 = 125 + 25 = 150 \] Point: (100, 150)
From these calculations, if you plot the points derived from these samples, you will see that the points (0, 25), (10, 37.5), (20, 50), (50, 87.5), and (100, 150) would appear on the graph of the function. The points will form a straight line since this is a linear function, starting at the point (0, 25), which is the fixed base cost of renting the truck, and increasing linearly as you drive more miles.
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