To determine which points correspond to the given linear function \( C = 1.25m + 25 \), we can plug in the values for \( m \) (miles driven) and calculate the total cost \( C \).
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For the point (4, 30): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(This point is valid)} \]
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For the point (8, 35): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \quad \text{(This point is valid)} \]
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For the point (2, 2.5): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(This point is not valid)} \]
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For the point (4, 5): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(This point is not valid)} \]
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For the point (30, 4): \[ C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \quad \text{(This point is not valid)} \]
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For the point (35, 8): \[ C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \quad \text{(This point is not valid)} \]
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For the point (2, 22.5): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(This point is not valid)} \]
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For the point (4, 20): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(This point is not valid)} \]
The points (4, 30) and (8, 35) are valid based on their calculations. So the answer is:
(4, 30) and (8, 35).