# How do you write an equation of a line given point (-6, 3) and has slope 2?

Oct 7, 2016

$y = 2 x + 15$

#### Explanation:

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

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

here m = 2 and $\left({x}_{1} , {y}_{1}\right) = \left(- 6 , 3\right)$

substitute these values into the equation

$y - 3 = 2 \left(x - \left(- 6\right)\right)$

$\Rightarrow y - 3 = 2 \left(x + 6\right) \Rightarrow y - 3 = 2 x + 12$

$\Rightarrow y = 2 x + 15 \leftarrow \text{ in slope-intercept form}$