Parallel Line Equation Calculator

Work out parallel line equation instantly with clear inputs, formula shown and shareable results.

About Parallel Line Equation Calculator

Parallel lines share the same gradient, so only the intercept changes. Substituting the given point into y = mx + c gives c = y₁ − m·x₁.

Formula

Parallel line

same m, new c = y₁ − m·x₁

Worked example

With the default values below, Parallel Line Equation Calculator returns Equation of the parallel line of y = 2x + 1. Change any input above and every figure here is recalculated in your browser.

Inputs used

Gradient of the original line: 2
Point x₁ on the new line: 3
Point y₁: 7

Results

Equation of the parallel line: y = 2x + 1
Gradient (unchanged): 2.00000000
New y-intercept: 1.00000000
Value of y where x = 0: 1.00000000

Step by step

1Values used
2Parallel line
3Equation of the parallel line= y = 2x + 1
4Gradient (unchanged)= 2.00000000
5New y-intercept= 1.00000000
6Value of y where x = 0= 1.00000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Line parallel to gradient 2 through (3, 7)?

c = 7 − 6 = 1, so y = 2x + 1.

Can two parallel lines ever meet?

Not in Euclidean geometry. Equal gradients with different intercepts means no solution to the pair of equations.