Find the slope of a line that is perpendicular to the line x + 3y - 5 = 0.

The perpendicular line would have a slope of 3.

Perpendicular lines have opposite and reciprocal slopes. So first we have to find the slope of the original line. We can do this by solving the equation for y.

x + 3y - 5 = 0

3y - 5 = -x

3y = -x + 5

y = -1/3x + 5/3

To do the opposite, take the original slope (-1/3) and change the sign (1/3).

To do the reciprocal, take the slope we changed (1/3) and flip it as a fraction (3).

This gives us a new slope of 3.