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

Apr 5, 2017

$y - 1 = - 6 \left(x - 5\right)$

#### 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 $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\text{where " (x_1,y_1),(x_2,y_2) " are 2 coordinate points}$

$\text{The 2 points here are " (4,7)" and } \left(5 , 1\right)$

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

$\Rightarrow m = \frac{1 - 7}{5 - 4} = \frac{- 6}{1} = - 6$

$\text{For " (x_1,y_1)" use either of the 2 given points}$

$\text{Using " m=-6" and } \left({x}_{1} , {y}_{1}\right) = \left(5 , 1\right)$

$\Rightarrow y - 1 = - 6 \left(x - 5\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$