If you drive the truck 100 mile the cost will be $70. If you drive the truck 175 miles the cost will be $73.75.

Question

Write a linear equation that models the cost, c in terms of the number of miles driven, m.

Answer 1

In this problem, you're given two pairs of data and asked to find a linear equation that they fit. Each pair of data can be represented by a point (m, c) representing miles and cost. You can apply everything you've learned to problems with x and y and drawing lines to this problem.

 

Your two data points are (miles, cost):

(100, $70)

(175, $73.75)

 

To find the equation of the line that fits these, you first need to find the rate of change (slope), and then use the equation of the line to find the fixed cost (y-intercept).

 

slope = (73.75-70)/(175-100)

 = 3.75/75

 = 0.05

 

General form of a line:

c = (slope) m + b

c = 0.05m + b

 

To find b, we can plug in one of the points we know:

 

70 = 0.05*(100) + b

70 = 5 + b

b = 65

 

Therefore, the equation of the line that models this cost is:

 

c = 0.05m + 65

 

Hope this helps, please comment if you're confused or have more questions!