What is the slope of a line?

The slope of a line measures its steepness and is the ratio of vertical change (rise) to horizontal change (run) between any two points: m = (y₂ − y₁)/(x₂ − x₁). A horizontal line has slope 0; a vertical line has undefined slope.

What is the slope-intercept form of a line?

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It is the most common way to write a linear equation and makes graphing straightforward.

How do you find the equation of a line from two points?

First compute the slope m = (y₂ − y₁)/(x₂ − x₁). Then substitute m and one of the points into y = mx + b and solve for b. The resulting equation is the line's slope-intercept form.

How are slopes of parallel and perpendicular lines related?

Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have slopes that multiply to −1 (m₁ · m₂ = −1), meaning they are negative reciprocals of each other. A vertical and horizontal line are perpendicular in a geometric sense, though the vertical slope is undefined.

Lines and Slopes: Tutorials, Graphers & Practice

Slope of a Line

Slope of a Line: Definition, Formula & Interactive Guide
An interactive tutorial on computing slope, interpreting rise-over-run, and identifying horizontal and vertical lines.
Slope Intercept Form y = mx + b: Formula, Examples & Practice
Understand how slope and y-intercept combine to define a line, with conversions from standard and point-slope forms.

Equation of a Line

Equations of Lines in Different Forms
Compare the point-slope, slope-intercept, and standard forms and learn when each is most useful.
General Equation of a Line: ax + by = c
Work with the general (standard) form and find its intercepts and slope directly from the coefficients.
Find Equation of a Line from a Graph
Read the slope and y-intercept off a graph and write the line's equation with confidence.

Parallel and Perpendicular Lines

Slopes of Parallel Lines: Proofs, Formulas, and Practice
Prove that parallel lines have equal slopes, and practice identifying parallel pairs from coordinates.
Slopes of Perpendicular Lines: Proof, Formulas, and Practice
Use the negative-reciprocal rule for perpendicular slopes, with proofs and worked exercises.

Slope and Line Practice Problems

Slope of a Line: Practice Questions with Solutions
Step-by-step solved problems on slope, rising/falling lines, horizontal/vertical lines, and parallel/perpendicular classification.
Equation of a Line – Practice Questions with Solutions
Practice finding equations from given slopes and points, with full solutions for every exercise.
More Slope Problems with Solutions
Additional solved slope problems covering perpendicular and parallel lines, distances, and graphing.
Math Questions with Answers (6): Slope and Lines
A quick self-check quiz covering slope, line equations, and parallel/perpendicular reasoning.

Slope and Line Calculators

Line Slope Calculator (from 2 points)
Enter two points and get the slope, equation, and intercepts instantly.
Slope-Intercept Line Calculator
Plot and analyze any line given in slope-intercept form y = mx + b.

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