# How do you write an equation of a line given point (1,-6) parallel to the line x+2y=6?

May 8, 2017

$y = - \frac{1}{2} x - \frac{11}{2}$

#### Explanation:

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

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

$\text{express " x+2y=6" in the form } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept

$\text{subtract x from both sides}$

$\cancel{x} \cancel{- x} + 2 y = 6 - x$

$\Rightarrow 2 y = 6 - x$

$\text{divide ALL terms by 2}$

$\frac{\cancel{2} y}{\cancel{2}} = \frac{6}{2} - \frac{1}{2} x$

$\Rightarrow y = - \frac{1}{2} x + 3 \leftarrow \text{ in form } y = m x + b$

$\Rightarrow \text{slope } = m = - \frac{1}{2}$

$\text{using " m=-1/2" and the point } \left(1 , - 6\right)$

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

$\text{to find b, substitute point into equation}$

$- 6 = - \frac{1}{2} + b \Rightarrow b = - \frac{11}{2}$

$\Rightarrow y = - \frac{1}{2} x - \frac{11}{2} \text{ is the equation}$