Question

A graph of the function y=80x+2 models Carli’s road trip, with her speed measured in miles per hour. The graph includes the two hours of stops she’ll make. Using this information, define which quantity describes the x-axis.
Responses:

time in hours

miles traveled

speed traveled

direction traveled

Answer 1

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

(2,22.5) and (4,20)

(4,30) and (8,35)

(2,2.5) and (4,5)

(30,4) and (35,8)

Answer 2

In the context of the function \( y = 80x + 2 \), where \( y \) represents speed in miles per hour and \( x \) represents time, the quantity that describes the x-axis is:

**time in hours**

This is because the variable \( x \) is typically used to represent the independent variable in the context of time in such scenarios.

Answer 3

To analyze the function \( C = 1.25m + 25 \), we can calculate the values for different mileages \( m \) and see which points might appear on the graph.

1. For \( m = 2 \):
\[
C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(not (2,22.5))}
\]

2. For \( m = 4 \):
\[
C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(not (4,20))}
\]

3. For \( m = 8 \):
\[
C = 1.25(8) + 25 = 10 + 25 = 35 \quad \text{(this matches (8,35))}
\]

4. For \( m = 30 \):
\[
C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \quad \text{(not (30,4))}
\]

5. For \( m = 35 \):
\[
C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \quad \text{(not (35,8))}
\]

Now let's summarize the evaluated points:
- **(2, 27.5)** is not listed.
- **(4, 30)** is a valid point.
- **(8, 35)** is a valid point.
- **(30, 62.5)** and **(35, 68.75)** do not match.

So, the points (4, 30) and (8, 35) would appear on the linear function, making the correct response:

**(4, 30) and (8, 35)**.