Question

Suppose a one-year subscription to a magazine costs $12.99 and a three-year subscription costs $25.98. The cost and length of a subscription are related. Write a slope-intercept equation to model the cost of a subscription for any period of time.

Answer 1

`y = 6.495x + 6.495`

Explanation:

Represent years with x and cost with y.

So, we have:

`(x_1,y_1)=(1,12.99)`

`(x_2,y_2)=(3,25.98)`

Required

Determine the slope intercept equation

First, we calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (25.98 - 12.99)/(3 - 1)`

`m = (12.99)/(2)`

`m = 6.495`

The equation is then calculated as:

`y - y_1 = m(x - x_1)`

Where

`m = 6.495`

`(x_1,y_1)=(1,12.99)`

`y - 12.99 = 6.495(x - 1)`

`y - 12.99 = 6.495x - 6.495`

Make y the subject

`y = 6.495x - 6.495 + 12.99`

`y = 6.495x + 6.495`