Question

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?

A: (2, 22.5) and ( 4, 20)

B: ( 30, 4) and ( 35, 8)

C: (2, 2.5) and ( 4, 5)

D: ( 4, 30) and ( 8, 35)

Answer 1

To find which points would appear on the graph of the linear function \( C = 1.25m + 25 \), we can calculate \( C \) (the total cost) for various values of \( m \) (the miles driven).

1. For \( m = 2 \):
\[
C = 1.25(2) + 25 = 2.5 + 25 = 27.5
\]
So, the point is \( (2, 27.5) \).

2. For \( m = 4 \):
\[
C = 1.25(4) + 25 = 5 + 25 = 30
\]
So, the point is \( (4, 30) \).

3. For \( m = 30 \):
\[
C = 1.25(30) + 25 = 37.5 + 25 = 62.5
\]
So, the point is \( (30, 62.5) \).

4. For \( m = 35 \):
\[
C = 1.25(35) + 25 = 43.75 + 25 = 68.75
\]
So, the point is \( (35, 68.75) \).

Now let's check the options:

A: \( (2, 22.5) \) and \( (4, 20) \) — Neither of these points are correct since we calculated \( (2, 27.5) \) and \( (4, 30) \).

B: \( (30, 4) \) and \( (35, 8) \) — Neither of these points are correct; we found higher costs for these mileages.

C: \( (2, 2.5) \) and \( (4, 5) \) — Again, these are incorrect based on our calculations.

D: \( (4, 30) \) and \( (8, 35) \) — The first point is correct; we calculated \( (4, 30) \), but for \( m = 8 \):
\[
C = 1.25(8) + 25 = 10 + 25 = 35
\]
So, \( (8, 35) \) is also correct.

Thus, the points that appear on the graph of the linear function are found in option D: **(4, 30) and (8, 35)**.