Point-Slope Form Calculator

Find the equation of a line using point-slope form. Enter a point and slope to get the equation in point-slope, slope-intercept, and standard forms.

Enter a point and slope to find the equation.

Point-Slope Form

y − y₁ = m(x − x₁)

The point-slope form is useful when you know one point on a line and the slope. It directly expresses the relationship between any point (x, y) on the line and the known point (x₁, y₁).

How to Use Point-Slope Form

  1. Identify a point (x₁, y₁) on the line.
  2. Identify the slope m.
  3. Substitute into y − y₁ = m(x − x₁).
  4. Simplify to get slope-intercept or standard form if needed.
Example: Point (2, 3), slope m = 4
Point-slope: y − 3 = 4(x − 2)
Slope-intercept: y = 4x − 5
Standard form: 4x − y = 5

Converting Between Forms

  • Point-slope → Slope-intercept: Expand and solve for y.
  • Point-slope → Standard: Expand, rearrange to ax + by = c.

FAQ

When should I use point-slope form?

Use it when you know a point and a slope but don't yet know the y-intercept. It's the quickest way to write the equation.

What if the slope is zero?

If m = 0, the line is horizontal: y = y₁.

Last updated: 2026-08-08