Problem

Let L₁ be the line ax + by = c, where a, b, and c are constants. What is the equation of the line perpendicular to L₁, passing through the point (0, c)?

Solution

To find the equation of the line we must first find the slope (call it m) of L₁, because the line perpendicular to L₁ has slope –1/m. To find the slope of L₁, we write the equation for L₁ is slope-intercept form:

and we can read off the slope:

Thus, our new line has slope

and therefore has the equation

for some constant p. We can solve for p using the fact that the point (0, c) is on our line. Plug the values x = 0, y = c into the equation:

So the equation of the line perpendicular to ax + by = c and pasing through (0, c) is