How do you write an equation in standard form given point (-2,4) and slope -3/2?

Jun 3, 2017

$3 x + 2 y = 2$

Explanation:

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

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

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=-3/2" and } \left({x}_{1} , {y}_{1}\right) = \left(- 2 , 4\right)$

$\Rightarrow y - 4 = - \frac{3}{2} \left(x + 2\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{rearrange terms into standard form}$

$y - 4 = - \frac{3}{2} x - 3$

$\Rightarrow \frac{3}{2} x + y = 1 \leftarrow \text{ multiply through by 2}$

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