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A rental truck company charges $25 to rent a truck, then $1.25 for every mile it is driven. The situation can be expressed as C=1.25m+25

, where C
is the total cost to rent the truck and m is the miles driven. If you plot points on the linear function, which of the following would appear?(1 point)
Responses

(30,4)
and (35,8)
left parenthesis 30 comma 4 right parenthesis and left parenthesis 35 comma 8 right parenthesis

(4,30)
and (8,35)
left parenthesis 4 comma 30 right parenthesis and left parenthesis 8 comma 35 right parenthesis

(2,22.5)
and (4,20)
left parenthesis 2,22.5 right parenthesis and left parenthesis 4 comma 20 right parenthesis

(2,2.5)
and (4,5)

1 answer

To determine which pairs of points lie on the given linear function \( C = 1.25m + 25 \), we can plug in the values of \( m \) (miles driven) from each point into the equation and check if we get the corresponding value of \( C \) (total cost).

  1. For point (30, 4):

    • Here, \( m = 4 \).
    • Calculating \( C \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \] So point (30, 4) is valid.

  2. For point (35, 8):

    • Here, \( m = 8 \).
    • Calculating \( C \): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \] So point (35, 8) is valid.

Now let's check the other pairs:

  1. For point (4, 30):

    • Here, \( m = 30 \).
    • Calculating \( C \): \[ C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \] So point (4, 30) is not valid.

  2. For point (8, 35):

    • Here, \( m = 35 \).
    • Calculating \( C \): \[ C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \] So point (8, 35) is not valid.

  3. For point (2, 22.5):

    • Here, \( m = 2 \).
    • Calculating \( C \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \] So point (2, 22.5) is not valid.

  4. For point (4, 20):

    • Here, \( m = 4 \).
    • Calculating \( C \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \] So point (4, 20) is not valid.

  5. For point (2, 2.5):

    • Here, \( m = 2.5 \).
    • Calculating \( C \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \] So point (2, 2.5) is not valid.

  6. For point (4, 5):

    • Here, \( m = 4 \).
    • Calculating \( C \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \] So point (4, 5) is not valid.

Only the first set of points—(30, 4) and (35, 8)—are valid according to the linear function \( C = 1.25m + 25 \).

Therefore, the answer is: (30, 4) and (35, 8).