Question

What is the equation of the line that goes through (5,- 3) and ( - 2, 9) ?

Answer 1

`y=-6/7x+9/7`

Explanation:

Plug the points into the equation to find slope:

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

Where:

`m=` slope

`(5,-3)=>(x_1,y_1)`

`(-2,9)=>(x_2,y_2)`

`m=(9-3)/(-2-5)=-6/7`

Now, using the slope of `-6/7` and a set of points (you choose which set of points to use, the equation will be the same either way), plug the numbers into the point slope formula

I'm going to use `(5,-3)`

`y-y₁=m(x-x₁)`

`m=` slope

`(5,-3)=>(x_1,y_1)`

`y+3=-6/7(x-5)`

Distribute `-6/7` throughout the set of parenthesis

`y+3=-6/7x+30/7`

Subtract the 3 from the left side of the equation so that it crosses out

`y=-6/7x+9/7`