Question

How do you write the equation in point slope form given ( -2 , 5 ) , ( 4 , -3 )?

Answer 1

Answers: `y-5=-4/3(x+2)` or `y+3=-4/3(x-4)`

Explanation:

Write point-slope form of a linear equation given points `(-2,5)` and `(4,-3)`.

Note that the general form of point-slope form is:
`y-y_1=m(x-x_1)` where `m` is the slope of the line and `(x_1,y_1)` is a point on the line.

First, we need to find the slope, m:
We know that `m=(y_2-y_1)/(x_2-x_1)` with points `(x_1,y_1)` and `(x_2,y_2)`
So, we can plug in our given values:
`m=(5-(-3))/(-2-4)`
`m=8/(-6)`
`m=-4/3`

Now, we choose one of the points to write the equation in point slope form, (I will write both possible equations in point-slope form):
For `(-2,5)`
`y-5=-4/3(x+2)`

For `(4,-3)`
`y+3=-4/3(x-4)`