Question

Explain how to write the equations of vertical lines, and why they are written this way

Answer 1

use the standard form ....

Answer 2

Ax + By = C

if we were to try to solve this for y we get:

y = -A/B x + C/B

equating this to the usual y = mx + b form, we see that the slope is defined as -A/B

but the slope of a vertical line is undefined, or rather, it is a division by 0, so B=0

substituting we find that

Ax + 0y = C or simply, Ax = C

as such x = C/A is the equation of a vertical line