The slope of the line through (2, 3) and (2, 7) is:

• A. 2
• B. 0
• C. Undefined
• D. -2

Answer: (C)

The slope tells how much y changes for a unit change in x. If a line goes straight up and down, x doesn’t change as you move along it, so you can’t form a finite ratio dy/dx. Here both points have the same x-coordinate, 2, so the line is vertical. Using the slope formula would give (7 − 3)/(2 − 2) = 4/0, which isn’t a defined value. That’s why vertical lines have undefined slope. The line through these points is x = 2, a vertical line, so the slope is undefined.