Linear Functions from Situations Quick Check

Question

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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Answer 1

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)