Suppose a line L has an equation Ax + By + C = 0.

Question

 What is the slope of L if B = 0 and A does not equal 0. 

Answer 1

First, setting B = 0 turns it into the equation:

Ax + C = 0

Ax = -C

x= -C/A

 

Given: Our A does not equal zero (phew!).

What we now have the general equation for a vertical line (x is always equal to -C/A, which is a constant, while the y value can be whatever it wants)

 

As such, the slope for the vertical line L is UNDEFINED.

Answer 2

Putting the equation into slope-intercept form, y = mx + b, shall indicate the slope, "m."

 

Ax + By + C = 0

Ax + By = -C

By = -Ax - C

y = -Ax/B - C/B

 

The slopes is -A/B.

 

Since B = 0, the slope is undefined. The line is vertical.