Geometry & Triangles

How to Find Slope Between Two Points

Slope is vertical change divided by horizontal change.

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Quick answer

Slope is vertical change divided by horizontal change.

Formula or method

m = (y₂ − y₁) ÷ (x₂ − x₁)

Keep units, percentages and time periods consistent. The formula is useful as a transparent check on the calculator result and helps explain why changing one input changes the answer.

Step-by-step

  1. Label the two points.
  2. Subtract y-values in one order.
  3. Subtract x-values in the same order.
  4. Divide rise by run.

Worked example

For (2,3) and (6,11), slope=(11−3)/(6−2)=2.

How to interpret the result

Positive slope rises left-to-right; zero is horizontal; a zero denominator is a vertical line with undefined slope.

When the answer is used for a purchase, loan, payroll decision, construction order, school grade, health estimate or other real-world choice, verify the assumptions that matter in that context. Accurate arithmetic still depends on accurate inputs.

Common mistakes

  • Changing subtraction order in only one part.
  • Calling vertical slope zero.
  • Mixing coordinate pairs.

Frequently asked questions

Horizontal slope?

Zero.

Vertical slope?

Undefined.

Does point order matter?

Not if used consistently.

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