# How do you write an equation in standard form for a line that goes through (5, –2) and (–5, 4)?

Aug 6, 2018

$3 x + 5 y = 5$

#### Explanation:

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

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

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

$\text{first, obtain the equation in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+c

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(5,-2)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 5 , 4\right)$

$m = \frac{4 - \left(- 2\right)}{- 5 - 5} = \frac{6}{- 10} = - \frac{3}{5}$

$y = - \frac{3}{5} x + c \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(5,-2)" then}$

$- 2 = - 3 + c \Rightarrow c = - 2 + 3 = 1$

$y = - \frac{3}{5} x + 1 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply all terms by 5}$

$5 y = - 3 x + 5$

$\text{add "3x" to both sides}$

$3 x + 5 y = 5 \leftarrow \textcolor{red}{\text{in standard form}}$