Line Equation Calculator
Find line equations from points, slope, or intercepts
Enter Two Points
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Theory & Formula
Line Equations
A line equation describes all points (x, y) that lie on a straight line. There are several ways to express a line equation, each useful in different contexts.
Slope
The slope (m) measures the steepness and direction of a line. It represents the rate of change of y with respect to x.
\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}\)
Forms of Line Equations
Slope-Intercept Form: \(y = mx + b\)
Where m is the slope and b is the y-intercept (where the line crosses the y-axis)
Point-Slope Form: \(y - y_1 = m(x - x_1)\)
Where m is the slope and (x₁, y₁) is a point on the line
Standard Form: \(Ax + By = C\)
Where A, B, and C are integers, and A is typically positive
Special Cases
- Horizontal line: \(m = 0\), equation is y = k (constant y-value)
- Vertical line: slope is undefined, equation is x = k (constant x-value)
- Parallel lines: have equal slopes (m₁ = m₂)
- Perpendicular lines: \(m_1 \cdot m_2 = -1\)