# How to write the slope intercept form of the equation of the line passes through (4,-1), and parallel y=2x-4?

Dec 18, 2016

$y = 2 x - 9$

#### Explanation:

Obtain the equation in $\textcolor{b l u e}{\text{point-slope form}}$ to begin with.

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

Note that $\textcolor{b l u e}{\text{parallel lines have equal slopes}}$

$y = 2 x - 4 \text{ is in " color(blue)"slope-intercept form}$

$\text{That is " y=mx+b larr " slope is m}$

$\Rightarrow \text{slope } = 2$

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

$y - \left(- 1\right) = 2 \left(x - 4\right) \Rightarrow y + 1 = 2 x - 8$

$\Rightarrow y = 2 x - 9 \text{ is equation in slope-intercept form}$