# How do you write the point slope form of the equation given (1,12) and (-3,5)?

May 9, 2017

$y - 12 = \frac{7}{4} \left(x - 1\right)$

#### Explanation:

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

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

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

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

$\text{the 2 points are } \left({x}_{1} , {y}_{1}\right) = \left(1 , 12\right) , \left({x}_{2} , {y}_{2}\right) = \left(- 3 , 5\right)$

$\Rightarrow m = \frac{5 - 12}{- 3 - 1} = \frac{- 7}{- 4} = \frac{7}{4}$

$\text{use either of the 2 given points as point on line}$

$\text{using "m=7/4" and "(x_1,y_1)=(1,12)" then}$

$y - 12 = \frac{7}{4} \left(x - 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$