# How do you write an equation of a point slope form passing through (-5,4) and parallel to the line whose equation is 4x-7y-8=0?

May 11, 2017

$y - 4 = \frac{4}{7} \left(x + 5\right)$

#### Explanation:

$\text{we require to know that}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{parallel lines have equal slope}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$\text{rearrange " 4x-7y-8=0" into this form}$

$\text{subtract 4x from both sides}$

$\cancel{4 x} \cancel{- 4 x} - 7 y - 8 = 0 - 4 x$

$\Rightarrow - 7 y - 8 = - 4 x$

$\text{add 8 to both sides}$

$- 7 y \cancel{- 8} \cancel{+ 8} = - 4 x + 8$

$\Rightarrow - 7 y = - 4 x + 8$

$\text{divide ALL terms by -7}$

$\frac{\cancel{- 7} y}{\cancel{- 7}} = \frac{- 4}{- 7} x + \frac{8}{- 7}$

$\Rightarrow y = \frac{4}{7} x - \frac{8}{7} \leftarrow \text{ in slope-intercept form}$

$\Rightarrow \text{slope } = m = \frac{4}{7}$

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

$\text{using " m=4/7" and " (x_1,y_1)=(-5,4)" then}$

$y - 4 = \frac{4}{7} \left(x - \left(- 5\right)\right)$

$\Rightarrow y - 4 = \frac{4}{7} \left(x + 5\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$