Point-Slope Form Calculator

Convert a point and slope into point-slope, slope-intercept, and standard form equations.

Enter Point & Slope

Point (x1, y1)

Result

Point-Slope Form
--
Slope-Intercept Form --
Standard Form (Ax + By = C) --
Slope (m) --
Y-Intercept --
X-Intercept --

Step-by-Step Solution

Understanding Point-Slope Form

Point-slope form is one of the most useful ways to write the equation of a line. Given a point (x1, y1) on the line and the slope m, the equation is written as y - y1 = m(x - x1). This form is particularly handy when you know a specific point and the rate of change.

Forms of Linear Equations

Point-Slope Form

Best when you know a point and the slope.

y - y1 = m(x - x1)

Slope-Intercept Form

Best for quickly identifying slope and y-intercept.

y = mx + b

Standard Form

Integer coefficients with A positive. Useful for certain algebraic operations.

Ax + By = C

Intercept Form

Uses both x and y intercepts.

x/a + y/b = 1

Converting Between Forms

Point-Slope to Slope-Intercept

  1. Start with y - y1 = m(x - x1)
  2. Distribute m: y - y1 = mx - mx1
  3. Add y1 to both sides: y = mx - mx1 + y1
  4. Simplify: y = mx + b, where b = y1 - mx1

Finding Intercepts

  • Y-intercept: Set x = 0 in the equation and solve for y. The point is (0, b).
  • X-intercept: Set y = 0 in the equation and solve for x. The point is (-b/m, 0).

When to Use Point-Slope Form

Point-slope form is ideal when you are given a point on a line and the slope, when finding the equation of a tangent line in calculus, when working with parallel or perpendicular lines (since you know the slope relationship), and when writing equations from word problems involving rates of change.