# What is the equation in point-slope form and slope intercept form for the line given (-3,6) and (2,-9)?

May 4, 2015

The point-slope form is $y - 6 = 3 \left(x + 3\right)$, and the slope-intercept form is $y = 3 x + 15$ .

Determine the slope, $m$.

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

Let $\left(- 3 , 6\right) = {x}_{1} , {y}_{1}$ and $\left(2 , - 9\right) = {x}_{2} , {y}_{2}$ .

$m = \frac{- 9 - 6}{2 - \left(- 3\right)} = \frac{15}{5} = 3$

Point-slope Form

The general formula is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Use one of the points given as ${x}_{1}$ and ${y}_{1}$. I'm going to use point $\left(- 3 , 6\right)$ which is consistent with finding the slope.

${x}_{1} = - 3$
${y}_{1} = 6$
$m = 3$.

$y - 6 = 3 \left(x - \left(- 3\right)\right)$ =

$y - 6 = 3 \left(x + 3\right)$

Slope-intercept Form

The general formula is $y = m x + b$, where $m$ is slope and $b$ is the y-intercept.

Solve the point-slope form equation for $y$.

$y - 6 = 3 \left(x + 3\right)$=

Add $6$ to both sides.

$y = 3 \left(x + 3\right) + 6$ =

Distribute the $3$.

$y = 3 x + 9 + 6$ =

$y = 3 x + 15$

The slope is $3$ and the $y$-intercept is $15$.