# How do you write the equation of a line that passes through the point (3, -6) and has a slope of 4?

May 20, 2017

$y = 4 x - 18$

#### Explanation:

$\text{the equation of a line in "color(blue)"point-slope form }$ 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 represent the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=4" and } \left({x}_{1} , {y}_{1}\right) = \left(3 , - 6\right)$

$y - \left(- 6\right) = 4 \left(x - 3\right)$

$\Rightarrow y + 6 = 4 \left(x - 3\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{distributing and simplifying gives another version}$

$y + 6 = 4 x - 12$

$\Rightarrow y = 4 x - 12 - 6$

$\Rightarrow y = 4 x - 18 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$