Slope & Equation of Line Calculator
Calculate slope and equation of a line from two points
Two Points
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Theory & Formula
Line Equations
A line in a coordinate plane can be described by various equation forms. The slope measures the steepness and direction of the line.
Slope Formula
The slope measures the rate of change between two points. Positive slope means the line rises, negative slope means it falls.
\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}\)
Equation Forms
Slope-Intercept Form: \(y = mx + b\)
where m is the slope and b is the y-intercept
Point-Slope Form: \(y - y_1 = m(x - x_1)\)
useful when you know the slope and one point
Standard Form: \(Ax + By = C\)
where A, B, and C are integers and A is positive
Special Cases
- Horizontal line: \(m = 0\), equation: y = k
- Vertical line: undefined slope, equation: x = h
- Parallel lines: have equal slopes
- Perpendicular lines: \(m_1 \cdot m_2 = -1\)