# How do you write the equation in point slope form given (0,8) and (-1,10)?

May 15, 2017

$y - 10 = - 2 \left(x + 1\right)$

#### 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 $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 coordinate points}$

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(0 , 8\right) , \left({x}_{2} , {y}_{2}\right) = \left(- 1 , 10\right)$

$\Rightarrow m = \frac{10 - 8}{- 1 - 0} = \frac{2}{- 1} = - 2$

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

$\text{using " m=-2" and } \left({x}_{1} , {y}_{1}\right) = \left(- 1 , 10\right)$

$y - 10 = - 2 \left(x - \left(- 1\right)\right)$

$\Rightarrow y - 10 = - 2 \left(x + 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$