An undefined slope occurs when a line is perfectly vertical. In such cases, the “run” (horizontal change) is zero, which makes the slope impossible to calculate mathematically.
Vertical lines:
- For a vertical line, the x-coordinate of every point on the line is the same.
- This means Δx=0 because there’s no horizontal change.
- When you plug 0 into the denominator of the slope formula, you get:
