# How do you find the parallel and perpendicular slope of 3x-5y=-8?

Jul 27, 2016

Parallel slope = $\frac{3}{5}$ and the perpendicular slope = $- \frac{5}{3}$

#### Explanation:

Change the equation of the line into standard form $y = m x + c$

$3 x - 5 y = - 8$

$3 x + 8 = 5 y$

$y = \frac{3}{5} x + \frac{8}{5}$

The slope of this line is $\frac{3}{5}$

Parallel lines have the same slope, so any line parallel to this one will have a a slope $m = \frac{3}{5}$

If lines are perpendicular, their slopes are negative reciprocals of each other and we can show:

${m}_{1} \times {m}_{2} = - 1$

To find the negative reciprocal, turn the slop upside down and change the sign.

So, for ${m}_{1} = \frac{3}{5} , \text{ } {m}_{2} = - \frac{5}{3}$