# How do you write the standard form of a line given (–3, 4) with a slope of 2?

Mar 20, 2017

$2 x - y = - 10$

#### Explanation:

The first step is to establish the equation of the line.

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

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

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

$y - 4 = 2 \left(x - \left(- 3\right)\right)$

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

The equation of a line in $\textcolor{b l u e}{\text{standard form}}$ 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.

$\text{Rearrange " y-4=2(x+3)" into this form}$

$y - 4 = 2 x + 6$

$\Rightarrow 2 x - y = - 10 \leftarrow \textcolor{red}{\text{ in standard form}}$