How do I write this in a linear equation?

Question

The number of dollars per month it costs you to own a car is a function of the number of kilometers per month you drive it. Based on the information in an issue of Time magazine, the cost varies linearly with the distance, and is $366 per month for 300 km per month, and $510 per month for 1500 km per month. Write the particular equation expressing cost (c) in terms of distance (d). 

Answer 1

d is the independent variable

c is the dependent variable

 

A linear function in the form   y=mx+b  , where m is slope and b is y-intercept.  To find the slope, we need two points.  From the information, our two points are in the form (d, c).

 

Point 1 = (300, 366)

Point 2 = (1500, 510)

 

 

Use the formula for slope:

 

m = (y₂ - y₁) / (x₂ - x₁)

 

m = (510 - 366) / (1500 - 300)

 

m = 144 / 1200 

 

m = 0.12

 

 

The equation of the line so far is

 

y = 0.12x + b

 

 

Plug in the values of the point 1 into the equation of the line to find b.

 

366 = 0.12(300) + b

 

366 = 36 + b

 

330 = b

 

 

The equation that we want is

 

c = 0.12d + 330