# How do you find a standard form equation for the line with x-intercept is -2, y-intercept is 7?

Jul 31, 2017

$7 x - 2 y = - 14$

#### Explanation:

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

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

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

$\text{given x-itercept } = \left(- 2 , 0\right)$

$\text{and y-intercept } = \left(0 , 7\right)$

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

•color(white)(x)y=mx+b

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

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

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

$\left({x}_{1} , {y}_{1}\right) = \left(- 2 , 0\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(0 , 7\right)$

$\Rightarrow m = \frac{7 - 0}{0 - \left(- 2\right)} = \frac{7}{2}$

$\Rightarrow y = \frac{7}{2} x + 7 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

$\text{rearrange into standard form}$

$\text{multiply through by 2}$

$\Rightarrow 2 y = 7 x + 14$

$\Rightarrow 7 x - 2 y = - 14 \leftarrow \textcolor{red}{\text{ in standard form}}$