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?

Question

A. (2, 2.5) and (4, 5)
B. (30, 4) and (35, 8)
C. (4, 30) and (8, 35)
D. (2, 22.5) and (4, 20)

Answer 1

To analyze which points would appear on the linear function \( C = 1.25m + 25 \), we can substitute the values of \( m \) from the given options into the equation to calculate \( C \).

1. Option A: (2, 2.5) and (4, 5)

   • For \( m = 2 \):
     \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \)
   • For \( m = 4 \):
     \( C = 1.25(4) + 25 = 5 + 25 = 30 \)
   • The points (2, 2.5) and (4, 5) do not appear.

2. Option B: (30, 4) and (35, 8)

   • For \( m = 30 \):
     \( C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \)
   • For \( m = 35 \):
     \( C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \)
   • The points (30, 4) and (35, 8) do not appear.

3. Option C: (4, 30) and (8, 35)

   • For \( m = 4 \):
     \( C = 1.25(4) + 25 = 5 + 25 = 30 \)
   • For \( m = 8 \):
     \( C = 1.25(8) + 25 = 10 + 25 = 35 \)
   • The points (4, 30) and (8, 35) do appear.

4. Option D: (2, 22.5) and (4, 20)

   • For \( m = 2 \):
     \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \)
   • For \( m = 4 \):
     \( C = 1.25(4) + 25 = 5 + 25 = 30 \)
   • The points (2, 22.5) and (4, 20) do not appear.

Based on the calculations above, the correct option where points will appear on the linear function is:

C. (4, 30) and (8, 35)