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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1 answer

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.

  1. For (30, 4):

    • C=30:
      30=1.25m+251.25m=5m=4
    • Valid point but not (30, 4).
  2. For (35, 8):

    • C=35: 35=1.25m+251.25m=10m=8
    • Valid point but not (35, 8).
  3. For (2, 22.5):

    • m=2: C=1.25(2)+25=2.5+25=27.5
    • Not valid since C should be 27.5.
  4. For (4, 20):

    • C=20: 20=1.25m+251.25m=5m=4
    • Not valid.
  5. For (2, 2.5):

    • m=2: C=1.25(2)+25=27.5
    • Not valid since C should be 27.5.
  6. 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)

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