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
𝐶
=
1.25
𝑚
+
25
, where C
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

(2,2.5)
(
2
,
2.5
)
and (4,5)
(
4
,
5
)
left parenthesis 2 comma 2.5 right parenthesis and left parenthesis 4 comma 5 right parenthesis

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

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

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

Answer 1

To determine which points would appear on the linear function \( C = 1.25m + 25 \), we can compute the value of \( C \) for various values of \( m \):

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

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

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

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

5. **For \( m = 8 \)**:
\[
C = 1.25(8) + 25 = 10 + 25 = 35
\]
The point is \( (8, 35) \).

6. **For \( m = 2 \)** (repeat):
We have already computed it as \( (2, 27.5) \).

After checking these calculations, we can review the provided options:

- \( (2, 2.5) \) and \( (4, 5) \) are not correct.
- \( (30, 4) \) and \( (35, 8) \) are not correct.
- \( (4, 30) \) is correct, but \( (8, 35) \) does not come from our previous calculations.
- \( (2, 22.5) \) and \( (4, 20) \) are not correct either.

From the calculations, it's clear that the only points matching from the equation would be \( (2, 27.5) \) and \( (4, 30) \). However, among the options given, **the closest points are \( (4, 30) \) and \( (8, 35) \)**, where \( (4, 30) \) is correct as per our calculations, while \( (8, 35) \) is just a miscalculation.

Thus, the relevant pair from the options is:
- \( (4, 30) \) and **(8, 35)** would be the closest to the points we calculated based on the distance formula provided.

So the best response based on provided points and calculations is **(4, 30)** as it accurately reflects part of the calculations shown.