Question

How do you write the slope-intercept form of the equation of the line that goes through `(2, -2)` and `(0, 3)`?

Answer 1

`y=-5/2x+3`

Explanation:

Slope intercept form of a line is:

`y=mx+b`

Where `m` is the slope and `b` is the `y` intercept

To write an equation using two sets of points, you first have to ind the slope:

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

Where
`(2,-2)=>(x_1,y_1)`

and

`(0,3)=>(x_2,y_2)`

`m=(3+2)/(0-2)=-5/2`

Next, pick a set of points and plug them into point slope formula using the slope of `-5/2`:

`y-y_1=m(x-x_1)`

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

Distribute the `-5/2` throughout the set of parenthesis

`y+2=-5/2x+5`

Subtract `2` on both sides of the parenthesis

`y=-5/2x+3`

If you were to use the other set of parenthesis, `(0,3)`, the equation should be the same

`y-3=-5/2(x-0)`

Distribute the `-5/2` throughout the set of parenthesis

`y-3=-5/2+0`

Add `3` on both sides of the equation

`y=-5/2+3`