Algebra 1 Intermediate

Point-Slope Form

Enter a point (x₁, y₁) and slope m to instantly write the equation in point-slope form, then convert to slope-intercept and standard form — with full step-by-step work and a live graph.

Live — instant results

Three equation forms

Step-by-step conversion + graph

Enter Point & Slope

x₁

y₁

Slope m (enter fractions as decimals, e.g. 0.5 for ½)

Rise over run — negative slope goes downhill left-to-right.

Please fill in all three fields (x₁, y₁, and m).

Examples

Equation Forms

Enter a point and slope, then click Convert to see all three equation forms here.

Step-by-Step Conversion

Graph

Point-Slope Form Explained

y − y₁ = m(x − x₁)

Point-slope form is built directly from the definition of slope. If you know a point (x₁, y₁) on a line and its slope m, you can write the equation immediately — no extra steps needed.

When to use it:

Given a point and a slope — write it straight away
Given two points — find the slope first, then use either point
Graphing a line when the y-intercept is not obvious
Writing a tangent line equation in pre-calculus / calculus

Any point on the line works as (x₁, y₁) — both give the same line, just written differently at first.

The Three Forms Compared

Every non-vertical line can be written in all three forms. Each has a different purpose:

Point-Slope y−y₁=m(x−x₁) — best when you know a point & slope; easiest to write first
Slope-Intercept y=mx+b — best for graphing; m and b are visible at a glance
Standard Form Ax+By=C — required on many tests; A, B, C are integers with A>0

Converting between forms is a core Algebra 1 skill tested on the SAT, state exams, and every subsequent math course.

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