# How do you write the equation in point slope form given (-6,-3), m=-1?

Aug 19, 2017

$y + 3 = - 1 \left(x + 6\right)$

#### Explanation:

$\text{the equation of a line in "color(blue)"point-slope form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\text{where m represents the slope and } \left({x}_{1} , {y}_{1}\right)$
$\text{a point on the line}$

$\text{here "m=-1" and } \left({x}_{1} , {y}_{1}\right) = \left(- 6 , - 3\right)$

$\Rightarrow y - \left(- 3\right) = - 1 \left(x - \left(- 6\right)\right)$

$\Rightarrow y + 3 = - 1 \left(x + 6\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

Aug 19, 2017

$y + 3 = - 1 \left(x + 6\right)$

#### Explanation:

The point-slope formula for a straight line is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

For $\left(- 6 , - 3\right) , m = - 1$

$y - \left(- 3\right) = - 1 \left(x - \left(- 6\right)\right)$

$y + 3 = - 1 \left(x + 6\right)$

This can be simplified to give the other forms:

$y = - x - 6 - 3$

$y = - x - 9 \text{ } \leftarrow$ this is slope-intercept form.

$x + y = - 9 \text{ } \leftarrow$ this is standard form