# What is the slope of a line perpendicular to 2y=-6x+8?

First we need to solve the linear equation for $y$ because we need to get the slope. Once we have the slope we need to convert it to its negative reciprocal, this means to just change the sign of the slope and flip it. The negative reciprocal is always perpendicular to the original slope.
$2 y = - 6 x + 8$
$y = \left(\frac{- 6 x}{2}\right) + \frac{8}{2}$
$y = - 3 x + 4$
The current slope is $- 3$ or $\frac{- 3}{1}$
The negative reciprocal is $\frac{1}{3}$.