# How do you write an equation in standard form given a line that passes through (5,-5) and (7,-2)?

Apr 8, 2018

$3 x - 2 y = 25$

#### Explanation:

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

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

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

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

•color(white)(x)y=mx+b

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(5,-5)" and } \left({x}_{2} , {y}_{2}\right) = \left(7 , - 2\right)$

$\Rightarrow m = \frac{- 2 - \left(- 5\right)}{7 - 5} = \frac{3}{2}$

$\Rightarrow y = \frac{3}{2} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(7,-2)" then}$

$- 2 = \frac{21}{2} + b \Rightarrow b = - \frac{4}{2} - \frac{21}{2} = - \frac{25}{2}$

$\Rightarrow y = \frac{3}{2} x - \frac{25}{2} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply all terms by 2}$

$\Rightarrow 2 y = 3 x - 25$

$\Rightarrow 3 x - 2 y = 25 \leftarrow \textcolor{red}{\text{in standard form}}$