# What is the standard form equation of the line passing through (–2, 8) with a slope of 2?

May 29, 2017

$2 x - y = - 12$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where A is a positive integer and B, C are integers.

$\text{find the equation firstly in "color(blue)"point-slope form}$

• y-y_1=m(x-x_1)
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=2" and } \left({x}_{1} , {y}_{1}\right) = \left(- 2 , 8\right)$

$\Rightarrow y - 8 = 2 \left(x + 2\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{rearrange into standard form}$

$y - 8 = 2 x + 4$

$y - 2 x = 4 + 8$

$\Rightarrow - 2 x + y = 12 \leftarrow \text{ multiply through by - 1}$

$\Rightarrow 2 x - y = - 12 \leftarrow \textcolor{red}{\text{ in standard form}}$