Writing Line Equations from Information

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

Learn with original explanations and worked examples. OpenStax Elementary Algebra 2e was consulted for topic coverage.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Algebra 1 · Unit 5 · Topic 5.3

Writing Line Equations from Information

Point-slope form y − y₁ = m(x − x₁) describes a nonvertical line through (x₁, y₁) with slope m.

Definition and explanation

Point-slope form y − y₁ = m(x − x₁) describes a nonvertical line through (x₁, y₁) with slope m. A second point can supply the slope when it is not already known.

Worked example

A line through (2, 5) with slope −3 has equation y − 5 = −3(x − 2). Expanding gives y = −3x + 11. At x = 2, the output is 5, as required.

Common mistake

A point's y-coordinate is not automatically the y-intercept unless its x-coordinate is zero.

Key takeaway

Point-slope form y − y₁ = m(x − x₁) describes a nonvertical line through (x₁, y₁) with slope m.

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.