# How do you write an equation of the line parallel to #x+2y=6 through (8,3)?

Oct 29, 2016

$y = - \frac{1}{2} x + \frac{19}{2}$

#### Explanation:

To write an equation of a straight line we have to determine its slope and a point it passes through.

Two straight lines are parallel if and only if they have same slope.

$x + 2 y = 6$

$\Rightarrow 2 y = 6 - x$

$\Rightarrow y = 3 - \frac{x}{2}$

The slope ight line is of the given strais $- \frac{1}{2}$
Because the two lines are parallel then they have same slope $- \frac{1}{2}$

Equation of a line passing through$\left(8 , 3\right)$and slope $- \frac{1}{2}$

$y - 8 = - \frac{1}{2} \left(x - 3\right)$

$y = - \frac{1}{2} x + \frac{3}{2} + 8$

$y = - \frac{1}{2} x + \frac{19}{2}$