Slope from Points and Graphs

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 5 · Topic 5.1

Slope from Points and Graphs

For two points with different x-coordinates, slope is m = (y₂ − y₁)/(x₂ − x₁).

Definition and explanation

For two points with different x-coordinates, slope is m = (y₂ − y₁)/(x₂ − x₁). It measures vertical change per horizontal change; horizontal lines have slope zero and vertical lines have undefined slope.

Worked example

Through (−2, 7) and (4, −5), the slope is (−5 − 7)/(4 − (−2)) = −12/6 = −2. An increase of 1 in x corresponds to a decrease of 2 in y along this line.

Common mistake

Keep the subtraction order the same in numerator and denominator.

Key takeaway

For two points with different x-coordinates, slope is m = (y₂ − y₁)/(x₂ − x₁).

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.