y=mx+bVariables
- m: slope of the line
- b: y-intercept
- x: horizontal coordinate
- y: vertical coordinate
How to use this formula
Expresses a straight line using its slope and vertical intercept.
Important notes
- A positive slope rises from left to right; a negative slope falls.
- The point (0, b) is where the line crosses the y-axis.
Quick example
The line y = 2x + 3 has slope 2 and y-intercept 3.
Applicability, worked calculation, and verification
Domain and applicability
Represents nonvertical straight lines in a Cartesian plane; vertical lines cannot be written with a finite slope m.
Units
- m has y-units per x-unit
- b and y use the same units
Assumptions and domain checks
- A positive slope rises from left to right; a negative slope falls.
- For the Slope-Intercept 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 Slope-Intercept Form when its variable definitions, domain restrictions, or structural assumptions differ from the problem.
Boundary and special cases
- For Slope-Intercept Form, check zero, negative, and extreme input values before relying on the result.
- When using Slope-Intercept 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=mx+b for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
For y = 2x + 3 and x = 4, the output is y = 2(4) + 3 = 11. The line crosses the y-axis at 3 and rises 2 units per 1 unit of run.
- Read the slope and intercept from the equation: m = 2 and b = 3.
- Substitute x = 4 into y = mx + b.
- Multiply 2 × 4 = 8, then add the intercept 3.
- Report the point on the line as (4, 11).
Independent verification
Using the intercept point (0, 3), the slope between (0, 3) and (4, 11) is (11 − 3)/(4 − 0) = 2, matching the equation.
Common mistakes
- Before substituting values into Slope-Intercept Form, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- For the Slope-Intercept Form, check the final value in the original equation; algebraic rearrangement can introduce or lose solutions when domains are restricted.
Continue the workflow
Use Slope-Intercept 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=mx+b. - 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 Slope-Intercept 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 Slope-Intercept Form used for?
Expresses a straight line using its slope and vertical intercept.
Can I copy this formula as LaTeX?
Yes. Copy y=mx+b 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.