Line Equation Calculator

Equation Through Two Points

Point A: x₁

Point A: y₁

Point B: x₂

Point B: y₂

Finds run, rise, slope, point-slope form, slope-intercept form, standard form, vectors, intercepts, and a graph.

Point-Slope Equation

Point x₁

Point y₁

Slope m

Uses y − y₁ = m(x − x₁). Fractions such as 3/2 are accepted. Use Standard Form for vertical lines.

Slope-Intercept Form

Slope m

Y-intercept b

Writes y = mx + b, converts to standard form, and identifies x- and y-intercepts.

Standard Form Analyzer

a in ax + by + c = 0

b in ax + by + c = 0

c in ax + by + c = 0

Converts standard equations into slope-intercept form when possible. It also handles vertical lines automatically.

Line From Axis Intercepts

X-intercept p

Y-intercept q

Uses x/p + y/q = 1. Both non-zero intercepts are required for this form.

Parallel Line Through a Point

Reference a

Reference b

Reference c

New point x

New point y

For reference line ax + by + c = 0, the parallel line keeps a and b unchanged.

Perpendicular Line Through a Point

Reference a

Reference b

Reference c

Required point x

Required point y

The tool creates a right-angle line through the requested point, including vertical and horizontal cases.

Intersection of Two Lines

L₁ coefficient a₁

L₁ coefficient b₁

L₁ constant c₁

L₂ coefficient a₂

L₂ coefficient b₂

L₂ constant c₂

Each line uses ax + by + c = 0. The calculator distinguishes unique, parallel, and coincident cases.

Angle Between Two Line Directions

L₁ coefficient a₁

L₁ coefficient b₁

L₂ coefficient a₂

L₂ coefficient b₂

Enter a and b from each ax + by + c = 0 line. Constants do not affect the angle.

Perpendicular Distance From a Point to a Line

Line coefficient a

Line coefficient b

Line constant c

Point x₀

Point y₀

Returns the shortest distance and the exact foot of the perpendicular segment on the line.

↗Line Equation Calculator

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