Slope of a Line Through Two Points

Quick answer: For distinct points with x₂ ≠ x₁, slope m = (y₂ − y₁)/(x₂ − x₁). A horizontal line has slope zero; a vertical line has undefined slope.

Worked example

Find the slope through (−1, 2) and (3, 10).

1. Change in y = 10 − 2 = 8.
2. Change in x = 3 − (−1) = 4.
3. m = 8/4 = 2.
4. The line rises 2 units for every unit moved right.

Check the result

Using point-slope form gives y − 2 = 2(x + 1); substituting x = 3 gives y = 10.

Common mistake to avoid

Use the same point order in numerator and denominator. Reversing only one changes the sign incorrectly.

Try it yourself

1. Find slope through (2, 5) and (6, 5). 2. Find slope through (3, 1) and (3, 7).

Answers and reasoning

1. 0/4 = 0, a horizontal line. 2. Division by zero occurs, so slope is undefined, not zero.

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