# If you are finding the line perpendicular to x + 3y = 5, what is the slope of the perpendicular line?

May 6, 2017

The slope of perpendicular line is $3$
$x + 3 y = 5 \mathmr{and} 3 y = - x + 5 \mathmr{and} y = - \frac{1}{3} x + \frac{5}{3}$. Comparing with standard equation $y = m x + c$ we get slope ${m}_{1} = - \frac{1}{3}$
The product of slopes of the perpendicular lines is $- 1 \therefore {m}_{1} \cdot {m}_{2} = - 1 \mathmr{and} {m}_{2} = - \frac{1}{m} _ 1 = - \frac{1}{- \frac{1}{3}} = 3$
The slope of perpendicular line is $3$ [Ans]