Question

What is the equation of the line passing through `(2,-8)` and `(5,-3)`?

Answer 1

The equation in slope intercept form is `y=5/3x-34/3`.

Explanation:

First find the slope, `m`.

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

`(x_1,y_1)=(2,-8)`

`(x_2,y_2)=(5,-3)`

`m=(-3-(-8))/(5-2)`

`m=(-3+8)/3`

`m=5/3`

Us the point slope form of a linear equation, `y-y_1=m(x-x_1)`, where `m` is the slope and `(x_1,y_1)` is one of the points on the line, such as `(2,-8)`.

`y-y_1=5/3(x-x_1)`

`y-(-8)=5/3(x-2)`

`y+8=5/3(x-2)`

Multiply both sides times `3`.

`3(y+8)=5(x-2)`

`3y+24=5x-10`

Subtract `24` from both sides.

`3y=5x-10-24`

`3y=5x-34`

Divide both sides by `3`.

`y=5/3x-34/3`