Standard Form Of A Line Calculator

Work out standard form of a line instantly with clear inputs, formula shown and shareable results.

About Standard Form Of A Line Calculator

Standard form Ax + By = C avoids fractions and handles vertical lines, which slope-intercept form cannot. Starting from y = mx + c, rearranging gives −mx + y = c, then multiplying through clears any fractions.

Formula

Standard form

y = mx + c ⇒ −mx + y = c ⇒ Ax + By = C

Worked example

With the default values below, Standard Form Of A Line Calculator returns Standard form Ax + By = C of -3x + 4y = 12. Change any input above and every figure here is recalculated in your browser.

Inputs used

Gradient m: 0.75
y-intercept c: 3
Multiply through byminimum 0: 4

Results

Standard form Ax + By = C: -3x + 4y = 12
A: -3.000000
B: 4.000000
C: 12.000000

Step by step

1Values used
2Standard form
3Standard form Ax + By = C= -3x + 4y = 12
4A= -3.000000
5B= 4.000000
6C= 12.000000

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 6 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

Convert y = 0.75x + 3 with a multiplier of 4.

−3x + 4y = 12, or equivalently 3x − 4y = −12.

Why prefer standard form?

It represents vertical lines such as x = 5 and keeps all coefficients as whole numbers, which suits solving systems.