Point-slope form

Math

Definition

A form of a linear equation that uses a known point (x₁, y₁) and the slope m to write the equation of a line. It is especially useful when you know the slope and one point but not the y-intercept.

Examples

  • A line through (2, 3) with slope 4: y - 3 = 4(x - 2)
  • Writing the equation of a tangent line in calculus
  • Finding a line through (1, -5) with slope -2: y + 5 = -2(x - 1)
Key Fact

y - y₁ = m(x - x₁)

Related Terms

Slope-intercept form Slope Standard form

Study This Concept

Practice point-slope form with free review games in these units:

Algebra 1 Unit 4: Writing Linear Equations