Slope of a line perpendicular to 5x -9y = 1

The perpendicular line would have a slope of 1/3.

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.

5x - 9y = 1

-9y = -5x + 1

y = 5/9x - 1/9

To do the opposite, take the original slope (5/9) and change the sign (-5/9).

To do the reciprocal, take the slope we changed (-5/9) and flip it as a fraction (-9/5).

This gives us a new slope of