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 of taking a cab for a trip of 4.5 miles, we will use the linear function you've provided:

\[ c = 0.75m + 4 \]

Where:
- \( c \) is the cost of the trip,
- \( m \) is the distance in miles.

Plugging in \( m = 4.5 \):

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

Calculating \( 0.75 \times 4.5 \):

\[
0.75 \times 4.5 = 3.375
\]

Now add 4 to that result:

\[
c = 3.375 + 4 = 7.375
\]

Rounding to the nearest hundredth:

\[
c \approx 7.38
\]

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

To graph the equation \( c = 0.75m + 4 \), you can plot the y-intercept (where \( m = 0 \), \( c = 4 \)) and another point (for example, \( m = 4 \), \( c = 4 + 3 = 7 \)). Then draw a line through these points. The slope of the line is 0.75, indicating that for every additional mile, the cost increases by $0.75.