Question

Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.

months costs
1 $1,859
3 $2,577
8 $4,372
12 $5,808

Answer 1

`y=359x+1500`

Explanation:

The data provided is as follows:

Months (x) Costs (y)

1 $1,859

3 $2,577

8 $4,372

12 $5,808

The slope intercept form is:

`y = mx+b`

Here,

m = slope

b = intercept.

Compute the value of m and b as follows:

`\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = ( 14616 \cdot 218 - 24 \cdot 114262)/( 4 \cdot 218 - 24^2) \approx 1500 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = ( 4 \cdot 114262 - 24 \cdot 14616 )/( 4 \cdot 218 - \left( 24 \right)^2) \approx 359\end{aligned}`

The equation in slope-intercept form to represent the total cost, y, of leasing a car for x months is:

`y=359x+1500`