To determine which points appear on the plot of the function \( C = 1.25m + 25 \), we need to check if the points given in the options satisfy this equation where \( m \) is the miles driven and \( C \) is the total cost.
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Option (4, 30):
- Plug \( m = 4 \) into the equation: \[ C = 1.25(4) + 25 = 5 + 25 = 30 \]
- This point is on the graph.
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Option (8, 35):
- Plug \( m = 8 \) into the equation: \[ C = 1.25(8) + 25 = 10 + 25 = 35 \]
- This point is also on the graph.
Since both points (4, 30) and (8, 35) satisfy the equation, we can confirm that this set of points would appear on the linear function.
Now let's check the other options for completeness:
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Option (2, 22.5):
- \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \) (not on the graph).
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Option (4, 20):
- \( C = 1.25(4) + 25 = 5 + 25 = 30 \) (not equal to 20).
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Option (2, 2.5):
- \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \) (not on the graph).
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Option (4, 5):
- \( C = 1.25(4) + 25 = 5 + 25 = 30 \) (not equal to 5).
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Option (30, 4):
- \( C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \) (not equal to 4).
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Option (35, 8):
- \( C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \) (not equal to 8).
Therefore, the points that would appear on the graph of the function are (4, 30) and (8, 35).