Question

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, 3).

Answer 1

`y-7=-(\displaystyle 4)/(\displaystyle 9)(x+4)`

OR

`y-3=-(\displaystyle 4)/(\displaystyle 9)(x-5)`

Explanation:

Hi there!

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

1) Determine the slope (m)

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

Plug in the given points (-4, 7) and (5, 3):

`m=(\displaystyle 3-7)/(\displaystyle 5-(-4))\\\\m=(\displaystyle 3-7)/(\displaystyle 5+4)\\\\m=(\displaystyle -4)/(\displaystyle 9)`

Therefore, the slope of the line is
`-(\displaystyle 4)/(\displaystyle 9)`. Plug this into
`y-y_1=m(x-x_1)` as
`m`:

`y-y_1=-(\displaystyle 4)/(\displaystyle 9)(x-x_1)`

2) Plug a point into
`y-y_1=-(\displaystyle 4)/(\displaystyle 9)(x-x_1)`

`y-y_1=-(\displaystyle 4)/(\displaystyle 9)(x-x_1)`

Because we're given two points, there are two ways we can write this equation:

`y-y_1=-(\displaystyle 4)/(\displaystyle 9)(x-x_1)\\\\y-7=-(\displaystyle 4)/(\displaystyle 9)(x-(-4))\\\\y-7=-(\displaystyle 4)/(\displaystyle 9)(x+4)`

OR

`y-3=-(\displaystyle 4)/(\displaystyle 9)(x-5)`

I hope this helps!