# How do you write the equation in point slope form given (3, 4) and (–3, –8)?

Sep 2, 2016

$y - 4 = 2 \left(x - 3\right)$

#### Explanation:

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

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

We require to find m. To do this we can use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m is the slope , $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points}$

The 2 points here are (3 ,4) and (-3 ,-8)

let $\left({x}_{1} , {y}_{1}\right) = \left(3 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 3 , - 8\right)$

$\Rightarrow m = \frac{- 8 - 4}{- 3 - 3} = \frac{- 12}{- 6} = 2$

We now have m = 2 and using either of the 2 given points, we can obtain the equation.

substitute m = 2 and $\left({x}_{1} , {y}_{1}\right) = \left(3 , 4\right) \text{ into (A)}$

$y - 4 = 2 \left(x - 3\right) \text{ equation in point-slope form}$