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

Jun 6, 2017

The point slope form is $y - 1 = - 8 \left(x + 2\right)$. 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

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

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

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

$m = \frac{1 - 9}{- 2 - \left(- 3\right)}$

Simplify.

$m = \frac{- 8}{- 2 + 3}$

$m = - 8$ or simply $- 8$

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

Point Slope Formula

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$,

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 $\left(- 2 , 1\right)$ as point 1.

Insert your values into the formula.

$y - 1 = - 8 \left(x - \left(- 2\right)\right)$

Simplify.

$y - 1 = - 8 \left(x + 2\right)$

We can solve the above equation.

$y - 1 = - 8 x - 16$

Add $1$ to both sides.

$y = - 8 x - 16 + 1$

$y = - 8 x - 15$

The above equation is in the slope intercept form : $y = m x + b$,

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