# How do you write an equation through point (-1,-8), perpendicular to y= -3/4x + 4?

Mar 16, 2017

$y = \frac{4}{3} x - \frac{20}{3}$

#### Explanation:

$y = - \frac{3}{4} x + 4 \text{ is in the form } \textcolor{red}{y = m x + b}$ where m represents the slope and b the y-intercept.

$\Rightarrow m = - \frac{3}{4}$

The slope of a perpendicular line is the $\textcolor{b l u e}{\text{negative reciprocal}}$ of the slope m.

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{3}{4}} = \frac{4}{3}$

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 $\left({x}_{1} , {y}_{1}\right) \text{ is a point on the line}$

$\text{here "m=4/3" and } \left({x}_{1} , {y}_{1}\right) = \left(- 1 , - 8\right)$

$\Rightarrow y - \left(- 8\right) = \frac{4}{3} \left(x - \left(- 1\right)\right)$

$\Rightarrow y + 8 = \frac{4}{3} \left(x + 1\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

Distributing the bracket and simplifying gives an alternative version of the equation.

$y + 8 = \frac{4}{3} x + \frac{4}{3}$

$\Rightarrow y = \frac{4}{3} x + \frac{4}{3} - 8$

$\Rightarrow y = \frac{4}{3} x - \frac{20}{3} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$