Find the gradient of the line joining the points (2, -3) and 2, 5)

Analyze the question: We need the gradient (slope) of the line through (2, -3) and (2, 5). The second point is written as "2, 5)", which is a typo for (2, 5).

Concept: Gradient = (y₂ − y₁) / (x₂ − x₁)

Solution:

• Point 1: (x₁, y₁) = (2, -3)
• Point 2: (x₂, y₂) = (2, 5)

m = (5 − (−3)) / (2 − 2) = 8 / 0

Division by zero is not defined, so the gradient is undefined.

Why this makes sense: Both points have the same x-coordinate (x = 2), so the line is a vertical line. A vertical line has no run (horizontal change is 0), and its gradient is undefined.

Checking the other options:

• A (9): not obtainable from any valid calculation here.
• B (1) and C (2): these would need a nonzero denominator. For example, 8/4 = 2 would need different x-values.
• D (undefined): matches our working.

Exam tip: Always compare the x-coordinates first.

• Same x-values → vertical line → gradient undefined.
• Same y-values → horizontal line → gradient 0.

This saves time and avoids careless errors.