Question

How do you write the equation in slope intercept form given (-2,-8) and (2,-6)?

Answer 1

`y=1/2x-9`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

m and b have to be found to complete the equation of the line.

To find m use the `color(blue)"gradient formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"`

Here the 2 points are (-2 ,-8) and (2 ,-6)

let `(x_1,y_1)=(-2,-8)" and " (x_2,y_2)=(2,-6)`

`rArrm=(-6-(-8))/(2-(-2))=2/4=1/2`

The same result is obtained if the coordinate points are reversed.

The partial equation is `y=1/2x+b`

To find b, use either of the 2 given points and substitute in the partial equation.
Using (2 ,-8) with x = 2 and y = -8

`(1/2xx2)+b=-8rArr1+b=-8rArrb=-9`

`rArry=1/2x-9" is the equation"`