Question

How do you find the point-slope form and slope-intercept form for a line with the two points `(-3,9)` and `(-2,1)`?

Answer 1

The point slope form is `y-1=-8(x+2)`. It can be solved for `y` to determine the slope intercept form: y=-8x-15#.
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Explanation:

First you'll need to get the slope, `m`, then you can get the equation of the line in point slope form.

Slope Formula

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

The two points are `(-3,9)` and `(-2,1)`. It doesn't matter which point you choose as 1 or 2. I'm going to use `(-3,9)` as point 1 and `(-2,1)` as point 2.

Insert the `x` and `y` values into the formula.

`m=(1-9)/(-2-(-3))`

Simplify.

`m=(-8)/(-2+3)`

`m=-8` or simply `-8`

Now you use the slope in the point slope formula for a straight line.

Point Slope Formula

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

where `x_1` and `y_1` make up a point. You can use either of the two points from above. I'm going to use `(-2,1)` as point 1.

Insert your values into the formula.

`y-1=-8(x-(-2))`

Simplify.

`y-1=-8(x+2)`

We can solve the above equation.

`y-1=-8x-16`

Add `1` to both sides.

`y=-8x-16+1`

`y=-8x-15`

The above equation is in the slope intercept form : `y=mx+b`,

where `m` is the slope, `-8`, and `b` is the y-intercept, `-15`