The perpendicular line would have a slope of -5/7.
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.
7x - 5y = -6
-5y = -7x - 6
y = 7/5x + 6/5
To do the opposite, take the original slope (7/5) and change the sign (-7/5).
To do the reciprocal, take the slope we changed (-7/5) and flip it as a fraction (-5/7).
This gives us a new slope of -5/7.
