Question

How do you write the equation of a line in point slope form and slope intercept form given points (-2, 6) (5, 1)?

Answer 1

Your point slope form formula is=
`y-y_1=m(x-x_1)`

Where `m` is representing your slope.

You need to find your `x_1, y_1, x_2` and `y_2`.
Your first point in the first bracket is `x_1`. Second point in the first bracket is your `y_1`. First point in the second bracket is `x_2` and second point in the second bracket is your `y_2`.

So,
`x_1= -2`
`y_1= 6`
`x_2= 5`
`y_2= 1`

You need to find the slope before you can put it into point slope form.

To find slope using points, the formula is=

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

So your slope is going to be=

`(1-6 )/ (5 - -2 )= -5/7`

Your slope is `-5/7`

Next step is to substitute points into your point slope formula.
This is going to be

`y-6= -5/7 (x- -2)` *Two negatives become a positive

Your point slope formula is equaled to

`y-6= -5/7 (x+2)`

To find slope intercept form first you have to eliminate the bracket.
To do so multiply everything in the bracket by -5/7.
Your equation will look like this

`y-6= -5/7x -10/7`

Next you have to isolate your y variable. To do so, add 6 to both sides.

`y-6+6= -5/7x -10/7+6`

This will leave you with your slope intercept form which is

`y= -5/7x -32/7`