How do you write the equation in point slope form given (1,3) and (3,-5)?

Mar 28, 2017

$y - 3 = - 4 \left(x - 1\right)$

Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

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

To find m use the $\textcolor{b l u e}{\text{gradient formula}}$

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

The 2 points here are (1 ,3) and (3 ,-5)

let $\left({x}_{1} , {y}_{1}\right) = \left(1 , 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 5\right)$

$\Rightarrow m = \frac{- 5 - 3}{3 - 1} = \frac{- 8}{2} = - 4$

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

$\text{Using " (x_1,y_1)=(1,3)" and } m = - 4$

$\Rightarrow y - 3 = - 4 \left(x - 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$