Question

What is the slope of a line that is perpendicular to the line whose equation is ax+by=c?

Answer 1

The perpendicular line will have a slope of b/a.

To find this, we first have to solve our equation for slope intercept form.

ax + by = c ----> subtract ax

by = -ax + c ----> divide by b

y = -a/bx + c/b.

So we know the slope of this equation to be -a/b. Since perpendicular lines have opposite and reciprocal slopes, we know we can simply flip the fraction and make it a negative to get the new slope of b/a.