y-y_1=m(x-x_1)Variables
- m: slope
- (x₁,y₁): known point
How to use this formula
Defines a line from one point and its slope.
Important notes
- Convert to slope-intercept form when a y-intercept is needed.
Quick example
Through (2,3) with slope 4: y−3=4(x−2).
Applicability, worked calculation, and verification
Domain and applicability
Apply Point-Slope Form only when the listed variables are defined, denominators are nonzero, and the problem satisfies the assumptions stated on this page.
Assumptions and domain checks
- Convert to slope-intercept form when a y-intercept is needed.
- For the Point-Slope Form, all variables must lie in the stated domain, and every denominator or inverse operation must be defined.
Do not use this formula when
- Do not use Point-Slope Form when its variable definitions, domain restrictions, or structural assumptions differ from the problem.
Boundary and special cases
- For Point-Slope Form, check zero, negative, and extreme input values before relying on the result.
- When using Point-Slope Form, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form y-y_1=m(x-x_1) for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
A line through (2,3) with slope 4 is y-3=4(x-2), which simplifies to y=4x-5.
- Insert m=4, x₁=2, and y₁=3.
- Distribute 4 to obtain y-3=4x-8.
- Add 3 to both sides to obtain y=4x-5.
Independent verification
The simplified line gives y=3 at x=2 and has slope 4.
Common mistakes
- Before substituting values into Point-Slope Form, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- For the Point-Slope Form, check the final value in the original equation; algebraic rearrangement can introduce or lose solutions when domains are restricted.
Continue the workflow
Use Point-Slope Form in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
y-y_1=m(x-x_1). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked workflow, and verification method for Point-Slope Form.
Verified against: OpenStax Algebra and Trigonometry
Automated quality check: Passed the core formula indexing gate.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Point-Slope Form used for?
Defines a line from one point and its slope.
Can I copy this formula as LaTeX?
Yes. Copy y-y_1=m(x-x_1) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.