# How to write an equation in standard form for a line through (4,3); slope 1/2?

May 30, 2018

$x - 2 y = - 2$

#### Explanation:

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

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

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

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

•color(white)(x)y=mx+b

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

$\text{here } m = \frac{1}{2}$

$y = \frac{1}{2} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(4,3)" into the partial equation}$

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

$y = \frac{1}{2} x + 1 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply through by 2}$

$2 y = x + 2$

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