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Calculation Machine

Point Slope Form Calculator

y − y₁ = m(x − x₁), converted to every other form.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Point-slope form
y + 3 = 2.5(x − 4)
Slope-intercept form
y = 2.5x − 13
Standard form
2.5x − y + 13 = 0
y-intercept
-13
x-intercept
5.2
Perpendicular slope
-0.4

Quick answer

Point-slope form writes a line as y − y₁ = m(x − x₁) using any point on it and the slope — the fastest form when you know one point.

The formula

y − y₁ = m(x − x₁)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • x₁4
  • y₁-3
  • Slope m2.5

Result

  • Point-slope formy + 3 = 2.5(x − 4)
  • Slope-intercept formy = 2.5x − 13
  • Standard form2.5x − y + 13 = 0
  • y-intercept-13
  • x-intercept5.2
  • Perpendicular slope-0.4

How to use the Point Slope Form Calculator

  1. 1Enter any point that lies on the line.
  2. 2Enter the slope.
  3. 3Copy whichever form your assignment or software expects.

Frequently asked questions

Which point should I use?

Any point on the line works — the different-looking equations all simplify to the same slope-intercept form.

How do I get a perpendicular line?

Use the negative reciprocal slope shown here with the same point.

About this calculator