Question

Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).

Answer 1

`y-6=-(\displaystyle 8)/(\displaystyle 5)(x+2)`

OR

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

Explanation:

Hi there!

Point-slope form:
`y-y_1=m(x-x_1)` where
`(x_1,y_1)` is a point and
`m` is the slope

1) Determine the slope

`m=(\displaystyle y_2-y_1)/(\displaystyle x_2-x_2)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (-2, 6) and (3,-2):

`m=(\displaystyle -2-6)/(\displaystyle 3-(-2))\\\\m=(\displaystyle -8)/(\displaystyle 3+2)\\\\m=-(\displaystyle 8)/(\displaystyle 5)`

Therefore, the slope of the line is
`-(\displaystyle 8)/(\displaystyle 5)`. Plug this into
`y-y_1=m(x-x_1)`:

`y-y_1=-(\displaystyle 8)/(\displaystyle 5)(x-x_1)`

2) Plug in a point
`(x_1,y_1)`

`y-y_1=-(\displaystyle 8)/(\displaystyle 5)(x-x_1)`

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

`y-6=-(\displaystyle 8)/(\displaystyle 5)(x-(-2))\\\\y-6=-(\displaystyle 8)/(\displaystyle 5)(x+2)`

OR

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

I hope this helps!