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

Dec 14, 2017

$2 x + 3 y = 6$

#### Explanation:

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

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

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

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

•color(white)(x)y=mx+b

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

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(3,0)" and } \left({x}_{2} , {y}_{2}\right) = \left(0 , 2\right)$

$\Rightarrow m = \frac{2 - 0}{0 - 3} = - \frac{2}{3}$

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

$\text{multiply through by 3}$

$\Rightarrow 3 y = - 2 x + 6$

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