# How do you write an equation in standard form for a line passing through (3, –6) and (–2, –1)?

May 13, 2018

$x + y = - 3$

#### Explanation:

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

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

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

$\text{to begin obtain the equation in "color(blue)"slope-intercept form}$
$\text{and rearrange into standard form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(3,-6)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 - 1\right)$

$\Rightarrow m = \frac{- 1 - \left(- 6\right)}{- 2 - 3} = \frac{5}{- 5} = - 1$

$\Rightarrow y = - x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(3,-6)" then}$

$- 6 = - 3 + b \Rightarrow b = - 6 + 3 = - 3$

$\Rightarrow y = - x - 3 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{add "x" to both sides}$

$\Rightarrow x + y = - 3 \leftarrow \textcolor{red}{\text{in standard form}}$