# How do you write the point slope form of the equation given (-5,-1) and (4,-7)?

Nov 1, 2017

$y + 7 = - \frac{2}{3} \left(x - 4\right)$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{to calculate m use the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(-5,-1)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , - 7\right)$

$\Rightarrow m = \frac{- 7 - \left(- 1\right)}{4 - \left(- 5\right)} = \frac{- 6}{9} = - \frac{2}{3}$

$\text{use either of the 2 points for } \left({x}_{1} , {y}_{1}\right)$

$\text{using } \left({x}_{1} , {y}_{1}\right) = \left(4 , - 7\right)$

$y - \left(- 7\right) = - \frac{2}{3} \left(x - 4\right)$

$\Rightarrow y + 7 = - \frac{2}{3} \left(x - 4\right) \leftarrow \textcolor{red}{\text{ in point-s;ope form}}$