Line Equation Calculator
Line Equation Calculator
Find equation of line from points, slope-intercept, or intercepts. Convert between slope-intercept, point-slope, and standard forms.
Line Equation Result
y = 1.333x + 0.333
Equation Forms:
Slope-Intercept
Point-Slope
Standard Form
Step-by-Step Calculation:
Line Properties:
Graph Visualization:
The line equation represents all points (x,y) that satisfy the linear relationship.
What is a Line Equation?
A line equation is a mathematical expression that describes all points on a straight line in a coordinate plane. It represents the relationship between x and y coordinates of every point on the line. Line equations are fundamental in algebra, geometry, physics, engineering, and many other fields for modeling linear relationships.
Line Equation Forms
Slope-Intercept
m = slope
b = y-intercept
Point-Slope
Uses point & slope
Easy conversion
Standard Form
A, B, C integers
A ≥ 0, no fractions
Intercept Form
a = x-intercept
b = y-intercept
Line Equation Formulas
1. Slope Calculation from Two Points
Formula for slope between points (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁)
Where: x₂ ≠ x₁ (not vertical)
Positive m: Line rises left to right
Negative m: Line falls left to right
m = 0: Horizontal line
m undefined: Vertical line
2. Slope-Intercept Form (y = mx + b)
The most common line equation form:
y = mx + b
m = slope (rise/run)
b = y-intercept (where line crosses y-axis)
To find b: b = y - mx (using any point)
Example: y = 2x + 3 (slope=2, y-intercept=3)
3. Point-Slope Form Conversion
Converting point-slope to slope-intercept:
y - y₁ = m(x - x₁)
y = m(x - x₁) + y₁
y = mx - mx₁ + y₁
y = mx + (y₁ - mx₁)
So: b = y₁ - mx₁
Example: y - 3 = 2(x - 1) → y = 2x + 1
Line Properties Table
| Property | Formula | Description | Example |
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