# How do you write the standard form of a line given x intercept = 3, y intercept = 2?

May 27, 2017

$2 x + 3 y - 6 = 0$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y + C = 0} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where A is a positive integer and B, C are integers.

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

• y=mx+b " where m represents the slope and b, the"
$\textcolor{w h i t e}{\times \times \times \times \times x} \text{y-intercept}$

$\text{here " b=2} \mathmr{and} m = - \frac{2}{3}$

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

$\text{add " 2/3x" to both sides}$

$\frac{2}{3} x + y = \cancel{- \frac{2}{3} x} \cancel{+ \frac{2}{3} x} + 2$

$\Rightarrow \frac{2}{3} x + y = 2$

$\text{subtract 2 from both sides}$

$\frac{2}{3} x + y - 2 = 0$

$\text{multiply ALL terms by 3}$

$\Rightarrow 2 x + 3 y - 6 = 0 \leftarrow \textcolor{red}{\text{ in standard form}}$