# How do you write an equation in standard form for a line which passes through (–2, 6) and has a slope of –1?

Mar 20, 2018

$x + y = 4$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

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

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{here "m=-1" and } \left({x}_{1} , {y}_{1}\right) = \left(- 2 , 6\right)$

$\Rightarrow y - 6 = - 1 \left(x + 2\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

$\Rightarrow y - 6 = - x - 2$

$\Rightarrow x + y = 4 \leftarrow \textcolor{red}{\text{in standard form}}$