Point Slope Form Calculator

Work out point slope form instantly with clear inputs, formula shown and shareable results.

About Point Slope Form Calculator

Point-slope form y − y₁ = m(x − x₁) is the most direct way to write a line through a known point with a known gradient. Expanding it gives slope-intercept form with c = y₁ − m·x₁.

Formula

Point-slope form

y − y₁ = m(x − x₁)

Worked example

With the default values below, Point Slope Form Calculator returns Point-slope form of y + 2 = 0.5(x - 4). Change any input above and every figure here is recalculated in your browser.

Inputs used

Point x₁: 4
Point y₁: -2
Gradient m: 0.5

Results

Point-slope form: y + 2 = 0.5(x - 4)
Slope-intercept form: y = 0.5x - 4
y-intercept: -4.00000000
x-intercept (0 if horizontal): 8.00000000

Step by step

1Values used
2Point-slope form
3Point-slope form= y + 2 = 0.5(x - 4)
4Slope-intercept form= y = 0.5x - 4
5y-intercept= -4.00000000
6x-intercept (0 if horizontal)= 8.00000000

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 through (4, −2) with gradient 0.5?

y + 2 = 0.5(x − 4), which simplifies to y = 0.5x − 4.

When is point-slope preferable?

Whenever you have a point and a gradient, since it avoids the extra step of computing the intercept.