Question

What method can be used to write the equation of a line in slope-intercept form given two points?

Answer 1

`(y_2-y_1)/(x_2-x_1)` is slope and
`(y_1-(y_2-y_1)/(x_2-x_1)\,x_1)` is y-intercept of line.

Explanation:

Let the given two points are
`(x_1,y_1)\:and\:(x_2,y_2)`

First we find the equation using two point form then rewrite in Slope intercept form.

Equation of line using two piont form,

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-y_1=(y_2-y_1)/(x_2-x_1)\,x-(y_2-y_1)/(x_2-x_1)\,x_1`

`y=(y_2-y_1)/(x_2-x_1)\,x-(y_2-y_1)/(x_2-x_1)\,x_1+y_1`

`y=(y_2-y_1)/(x_2-x_1)\,x+(y_1-(y_2-y_1)/(x_2-x_1)\,x_1)`

here,
`(y_2-y_1)/(x_2-x_1)` is slope and
`(y_1-(y_2-y_1)/(x_2-x_1)\,x_1)` is y-intercept of line.