# How do you write the point slope form of the equation given (-4,1) parallel to y=-1/2x-1?

Apr 29, 2017

$y - 1 = - \frac{1}{2} \left(x + 4\right)$

#### Explanation:

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

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

$\text{require to know the following fact.}$

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

$y = - \frac{1}{2} x - 1 \text{ is in slope-intercept form, that is}$

$y = m x + b \Rightarrow \text{ slope } = m = - \frac{1}{2}$

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

$y - 1 = - \frac{1}{2} \left(x - \left(- 4\right)\right)$

$\Rightarrow y - 1 = - \frac{1}{2} \left(x + 4\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$