Question

The cost of taking a cab is $4 plus $0.75 per mile. This can be represented using the linear function c=0.75m+4
, where c is the cost per trip and m is the distance in miles. Graph the equation on a coordinate plane. Based on your line, what would the corresponding dependent variable be if you were to travel 4.5 miles? Round your answer to the nearest hundredth.

Answer 1

To find the cost \( c \) when traveling 4.5 miles, we can use the given linear function:

\[
c = 0.75m + 4
\]

Substituting \( m = 4.5 \):

\[
c = 0.75(4.5) + 4
\]

Calculating \( 0.75 \times 4.5 \):

\[
0.75 \times 4.5 = 3.375
\]

Now, add this to 4:

\[
c = 3.375 + 4 = 7.375
\]

Rounding to the nearest hundredth gives:

\[
c \approx 7.38
\]

So, if you were to travel 4.5 miles, the corresponding dependent variable (the cost) would be approximately **$7.38**.

To graph the equation \( c = 0.75m + 4 \), you would plot points for different distances \( m \) and their corresponding costs \( c \). For example:

- At \( m = 0 \): \( c = 4 \) (the starting fee)
- At \( m = 1 \): \( c = 4.75 \)
- At \( m = 2 \): \( c = 5.5 \)
- At \( m = 3 \): \( c = 6.25 \)
- At \( m = 4 \): \( c = 7 \)
- At \( m = 4.5 \): \( c = 7.38 \)
- At \( m = 5 \): \( c = 8 \)

You would then draw a straight line through these points, illustrating how the cost increases linearly with distance.