Question

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 480 mi and in June her cost was $460 for 800 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven. (a) Find a linear function C that models the cost of driving x miles per month. (b) Draw a graph of C. What is the slope of this line? (c) At what rate does Lynn's cost increase for every additional mile she drives?

Answer 1

Answer:

a) see attachment

b) Cost f(distance) = 0.25d + 260

c) $0.25

Step-by-step explanation:

b) The linear relationship between two variables is as follows:

C f(d) = m*d + k .... Eq 1

Where, m and k are constants to be evaluated

Find m: we will find slope of the line between two points (480,$380) & (800,$460)

Slope of line (m) = $\frac{460-380}{800-480}$ = $0.25 / mile

Find k: consider one of the two points and input in Eq 1 using (480,$380)

k = 380 - 0.25(480) = $260

The equation of line is C f(d) = 0.25*d +260.

We can use this equation for plotting the graph for part a

c) Rate of cost / mile is given by the slope of the graph if scruutinized on the units; hence, $0.25