Question
Linear Functions from Situations Quick Check
3 of 53 of 5 Items
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?(1 point)
Responses
(4,30) and (8,35)
left parenthesis 4 comma 30 right parenthesis and left parenthesis 8 comma 35 right parenthesis
(30,4) and (35,8)
left parenthesis 30 comma 4 right parenthesis and left parenthesis 35 comma 8 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)
left parenthesis 2 comma 2.5 right parenthesis and left parenthesis 4 comma 5 right parenthesis
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Answers
GPT-4o mini
To determine which points would appear on the linear function \( C = 1.25m + 25 \), we can plug in the values of \( m \) from each of the response options to see if the corresponding value for \( C \) matches the points provided.
1. **For (4, 30)**:
- \( m = 4 \):
\[
C = 1.25(4) + 25 = 5 + 25 = 30
\]
- This point is valid.
2. **For (8, 35)**:
- \( m = 8 \):
\[
C = 1.25(8) + 25 = 10 + 25 = 35
\]
- This point is also valid.
Thus, both points (4, 30) and (8, 35) are valid points on the function.
3. **For (30, 4)**:
- \( C = 30 \):
\[
30 = 1.25m + 25 \implies 1.25m = 5 \implies m = 4
\]
- Valid point but not (30, 4).
4. **For (35, 8)**:
- \( C = 35 \):
\[
35 = 1.25m + 25 \implies 1.25m = 10 \implies m = 8
\]
- Valid point but not (35, 8).
5. **For (2, 22.5)**:
- \( m = 2 \):
\[
C = 1.25(2) + 25 = 2.5 + 25 = 27.5
\]
- Not valid since \( C \) should be 27.5.
6. **For (4, 20)**:
- \( C = 20 \):
\[
20 = 1.25m + 25 \implies 1.25m = -5 \implies m = -4
\]
- Not valid.
7. **For (2, 2.5)**:
- \( m = 2 \):
\[
C = 1.25(2) + 25 = 27.5
\]
- Not valid since \( C \) should be 27.5.
8. **For (4, 5)**:
- \( m = 4 \):
\[
C = 1.25(4) + 25 = 30
\]
- Not valid since \( C \) should be 30.
Only **(4, 30)** and **(8, 35)** are valid points on the linear function.
**Final answer**: (4, 30) and (8, 35)
1. **For (4, 30)**:
- \( m = 4 \):
\[
C = 1.25(4) + 25 = 5 + 25 = 30
\]
- This point is valid.
2. **For (8, 35)**:
- \( m = 8 \):
\[
C = 1.25(8) + 25 = 10 + 25 = 35
\]
- This point is also valid.
Thus, both points (4, 30) and (8, 35) are valid points on the function.
3. **For (30, 4)**:
- \( C = 30 \):
\[
30 = 1.25m + 25 \implies 1.25m = 5 \implies m = 4
\]
- Valid point but not (30, 4).
4. **For (35, 8)**:
- \( C = 35 \):
\[
35 = 1.25m + 25 \implies 1.25m = 10 \implies m = 8
\]
- Valid point but not (35, 8).
5. **For (2, 22.5)**:
- \( m = 2 \):
\[
C = 1.25(2) + 25 = 2.5 + 25 = 27.5
\]
- Not valid since \( C \) should be 27.5.
6. **For (4, 20)**:
- \( C = 20 \):
\[
20 = 1.25m + 25 \implies 1.25m = -5 \implies m = -4
\]
- Not valid.
7. **For (2, 2.5)**:
- \( m = 2 \):
\[
C = 1.25(2) + 25 = 27.5
\]
- Not valid since \( C \) should be 27.5.
8. **For (4, 5)**:
- \( m = 4 \):
\[
C = 1.25(4) + 25 = 30
\]
- Not valid since \( C \) should be 30.
Only **(4, 30)** and **(8, 35)** are valid points on the linear function.
**Final answer**: (4, 30) and (8, 35)