# How do you write the point slope form of the equation given (4,2) and (1,-1)?

Mar 28, 2017

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

#### 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 calculate 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 (4 ,2) and (1 ,-1)

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

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

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

$\text{Using " (4,2)=(x_1,y_1)" and } m = 1$

$y - 2 = 1 \left(x - 4\right) \leftarrow \textcolor{red}{\text{ in point slope form}}$