Point Slope Form Calculator

This calculator finds the equation of a line in point-slope form (y - y₁ = m(x - x₁)) given a point and a slope.

Input Parameters

Calculation Results

Point Slope Form Equation

y - y₁ = m(x - x₁)

Where:
y₁ = Y-coordinate of the point
x₁ = X-coordinate of the point
m = Slope of the line

Slope-Intercept Form (Optional)

y = mx + b

Where b is the y-intercept calculated from the given point and slope.

Point Slope Form Calculator Usage Guide

Learn how to use the Point Slope Form Calculator and its working principles

What is Point Slope Form?

Point-slope form is a way to express the equation of a line. It is given by:

y - y₁ = m(x - x₁)

Where:

  • y₁ and x₁ are the coordinates of a specific point on the line
  • m is the slope of the line

How to Use This Calculator

  1. Enter the x-coordinate of your point in the "Point X₁" field
  2. Enter the y-coordinate of your point in the "Point Y₁" field
  3. Enter the slope of the line in the "Slope (m)" field
  4. Click the "Calculate" button to see the equation in point-slope form
  5. The calculator also provides the slope-intercept form (y = mx + b)

Example

Suppose you have a point (2, 3) and a slope of 4. The point-slope form would be:

y - 3 = 4(x - 2)

This represents the same line as the slope-intercept form y = 4x - 5.

Applications

Point-slope form is particularly useful when you know a single point on a line and its slope, but not necessarily its y-intercept. It can be easily converted to other forms:

  • From point-slope to slope-intercept: Solve for y to get y = mx + (y₁ - mx)
  • From point-slope to standard form: Rearrange to get mx - y = -mx + y₁