EZ Math

Algebra 1 · Linear functions and slope

How to Find the Slope of a Horizontal Line

Problem

(2,5) and (7,5)(2, 5) \text{ and } (7, 5)

Answer

m=0m = 0

A horizontal line never rises or falls, so its slope is zero. Do not confuse it with a vertical line, where the run is zero and the slope is undefined.

Step-by-step solution

  1. Write the slope formula.

    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

    Why: Slope is the change in y divided by the change in x.

  2. Substitute the two points.

    m=5−57−2=05m = \frac{5 - 5}{7 - 2} = \frac{0}{5}

    Why: Both points share the same y-value, so the rise is zero.

  3. Simplify.

    m=0m = 0

    Why: Zero divided by a nonzero number is zero, and a flat line has no steepness.

Common mistakes

  • Calling the slope undefined. That happens on a vertical line, where x does not change.
  • Writing 5 / 0 because the y-values match.
  • Skipping the subtraction and reporting the y-value, 5.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. (1,3) and (8,3)(1, 3) \text{ and } (8, 3)

    Show answer

    m=0m = 0

  2. (4,−2) and (9,−2)(4, -2) \text{ and } (9, -2)

    Show answer

    m=0m = 0

  3. (2,5) and (2,9)(2, 5) \text{ and } (2, 9)

    Show answer

    undefined\text{undefined}

  4. (−1,2) and (3,2)(-1, 2) \text{ and } (3, 2)

    Show answer

    m=0m = 0

  5. (2,−5) and (6,−5)(2, -5) \text{ and } (6, -5)

    Show answer

    m=0m = 0