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.(1 point)

Answer 1

To graph the equation \( c = 0.75m + 4 \) and find the corresponding cost for traveling 4.5 miles, we can start by plugging in \( m = 4.5 \) into the equation.

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

Calculating \( 0.75 \times 4.5 \):

\[
0.75 \times 4.5 = 3.375
\]

Now add 4:

\[
c = 3.375 + 4 = 7.375
\]

Rounding to the nearest hundredth, the corresponding cost \( c \) for traveling 4.5 miles would be:

\[
\text{Cost} \approx 7.38
\]

Thus, the dependent variable, or the cost for traveling 4.5 miles, is **$7.38**.

To graph the equation, you would create a coordinate plane with the x-axis representing miles (m) and the y-axis representing cost (c). The line would start at \( c = 4 \) when \( m = 0 \) (the base fare) and increase with a slope of \( 0.75 \). You would plot points based on various distances (e.g., (0, 4), (1, 4.75), (2, 5.50), (3, 6.25), (4.5, 7.375), etc.) and connect them to form a straight line.