# How do you write the equation of a line given point (6,5 ) and are parallel to and perpendicular to the line with equation y + 5x=8?

Sep 5, 2017

Parallal line is $y = - 5 x + 35$ and perpendiclur line is
$y = \frac{1}{5} x + \frac{19}{5}$

#### Explanation:

The slope of the line $y + 5 x = 8 \mathmr{and} y = - 5 x + 8$ is

 m= -5 ; [y=mx+c] . Parallal lines have equal slope i.e #-5)

and the product of slopes of perpendiclur lines is $- 1 \therefore m = \frac{1}{5}$.

The equation of line passing through $\left({x}_{1} , {y}_{1}\right)$ is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$.

The equation of line passing through $\left(6 , 5\right)$ , parallal to line

$y = - 5 x + 8$ is $y - 5 = - 5 \left(x - 6\right) \mathmr{and} y = - 5 x + 35$ and

the equation of line passing through $\left(6 , 5\right)$ , perpedicular to

line $y = - 5 x + 8$ is $y - 5 = \frac{1}{5} \left(x - 6\right) \mathmr{and} y = \frac{1}{5} x - \frac{6}{5} + 5$ or

$y = \frac{1}{5} x + \frac{19}{5}$ [Ans]