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 $450 for 830 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

Answer 1

Answer: the model is

C(x) = 0.2x + 284

Step-by-step explanation:

let x represent the distance driven in a month.

Let y represent the monthly cost for driving x miles.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (450 - 380)/(830 - 480)

m = 70/350 = 0.2

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 480, y = 380 and m = 0.2 into y = mx + c. It becomes

380 = 0.2 × 480 + c

380 = 96 + c

c = 380 - 96

c = 284

Therefore, the linear model is

y = 0.2x + 284

C(x) = 0.2x + 284