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How to Find the Slope of a Line

Learn how to find slope from two points, a graph, or an equation, with examples, common mistakes, troubleshooting, and FAQs.

EducationEdited by Pramod Tiwari
2 min read

Quick Answer

To find slope, use rise over run. From two points, subtract the y-values and divide by the difference in x-values: slope = (y2 - y1) / (x2 - x1).

What You Need

  • Two points, graph, or equation
  • Subtraction skills
  • Fraction simplification
  • Graph paper if using a graph

Safety Precautions

  • Keep point order consistent in numerator and denominator.
  • Do not divide by zero; vertical lines have undefined slope.
  • Remember horizontal lines have slope 0.
  • Check signs carefully.

Step-by-Step Instructions

  1. Step 1

    Identify two points

    Choose two clear points on the line.

  2. Step 2

    Label coordinates

    Write them as (x1, y1) and (x2, y2).

  3. Step 3

    Find rise

    Subtract y-values: y2 - y1.

  4. Step 4

    Find run

    Subtract x-values in the same order: x2 - x1.

  5. Step 5

    Divide rise by run

    Write slope as rise over run.

  6. Step 6

    Simplify

    Reduce the fraction if possible.

  7. Step 7

    Check direction

    A line rising left to right has positive slope; falling has negative slope.

Practical Example

Example: Points (2, 3) and (6, 11) have slope (11 - 3) / (6 - 2) = 8 / 4 = 2.

Common Mistakes

  • Switching point order halfway
  • Putting run over rise
  • Missing negative signs
  • Dividing by zero
  • Calling vertical slope zero
  • Not simplifying

Troubleshooting

Denominator is zero

The line is vertical, so slope is undefined.

Numerator is zero

The line is horizontal, so slope is 0.

Slope sign seems wrong

Check whether the line rises or falls from left to right.

Graph points are unclear

Choose two points where the line crosses grid intersections.

FAQs

What does slope mean?

Slope describes how steep a line is and whether it rises or falls.

What is rise over run?

Rise is vertical change and run is horizontal change.

What is the slope of a horizontal line?

The slope is 0.

What is the slope of a vertical line?

It is undefined because the run is zero.

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