# How do you write an equation in standard form given a line that passes through (5,22) and (3,12)?

May 7, 2018

$5 x - y = 3$

#### Explanation:

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

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

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

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

•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)

$\text{let "(x_1,y_1)=(5,22)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 12\right)$

$\Rightarrow m = \frac{12 - 22}{3 - 5} = \frac{- 10}{- 2} = 5$

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

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

$\text{using "(3,12)" then}$

$12 = 15 + b \Rightarrow b = 12 - 15 = - 3$

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

$\text{subtract y and add 3 to both sides}$

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