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

(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

(30,4)
and (35,8)
left parenthesis 30 comma 4 right parenthesis and left parenthesis 35 comma 8 right parenthesis
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Answer 1

To determine which points appear on the plot of the function \( C = 1.25m + 25 \), we need to check if the points given in the options satisfy this equation where \( m \) is the miles driven and \( C \) is the total cost.

1. Option (4, 30):

   • Plug \( m = 4 \) into the equation: \[ C = 1.25(4) + 25 = 5 + 25 = 30 \]
   • This point is on the graph.

2. Option (8, 35):

   • Plug \( m = 8 \) into the equation: \[ C = 1.25(8) + 25 = 10 + 25 = 35 \]
   • This point is also on the graph.

Since both points (4, 30) and (8, 35) satisfy the equation, we can confirm that this set of points would appear on the linear function.

Now let's check the other options for completeness:

3. Option (2, 22.5):

   • \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \) (not on the graph).

4. Option (4, 20):

   • \( C = 1.25(4) + 25 = 5 + 25 = 30 \) (not equal to 20).

5. Option (2, 2.5):

   • \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \) (not on the graph).

6. Option (4, 5):

   • \( C = 1.25(4) + 25 = 5 + 25 = 30 \) (not equal to 5).

7. Option (30, 4):

   • \( C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \) (not equal to 4).

8. Option (35, 8):

   • \( C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \) (not equal to 8).

Therefore, the points that would appear on the graph of the function are (4, 30) and (8, 35).