Calculate the slope of a line between two points
Basic Formula:
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope, (x₁, y₁) is the first point, and (x₂, y₂) is the second point.
Rise Over Run:
m = Rise / Run = Δy / Δx
Rise is the vertical change (Δy) and run is the horizontal change (Δx).
Angle of Inclination:
θ = arctan(m)
The angle the line makes with the positive x-axis, measured in degrees.
Positive Slope (m > 0)
Line rises from left to right. As x increases, y increases.
Negative Slope (m < 0)
Line falls from left to right. As x increases, y decreases.
Zero Slope (m = 0)
Horizontal line. y-value remains constant regardless of x.
Undefined Slope
Vertical line. x-value remains constant, division by zero.
Two lines are parallel if they have the same slope. Parallel lines never intersect and maintain a constant distance from each other.
Two lines are perpendicular if the product of their slopes equals -1. If one line has slope m, a perpendicular line has slope -1/m (negative reciprocal).
The equation y = mx + b represents a line where m is the slope and b is the y-intercept (where the line crosses the y-axis).
The equation y - y₁ = m(x - x₁) represents a line with slope m passing through point (x₁, y₁). Useful when you know a point and the slope.
Calculate percentages and percentage changes
Calculate percentage increase
Calculate percentage decrease
Calculate percentage difference
Calculate with fractions
Calculate ratios and proportions