Slope Calculator
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Step-by-Step Solution
About Slope Calculation
The slope of a line is a measure of its steepness and direction. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Slope Formulas
Slope Formula from Two Points
For two points (x₁, y₁) and (x₂, y₂), the slope m is:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Slope from Standard Form Equation
For a line in standard form Ax + By = C:
$m = -\frac{A}{B}$ (when B ≠ 0)
Slope from Slope-Intercept Form
For a line in slope-intercept form y = mx + b:
The slope is the coefficient m.
Parallel and Perpendicular Lines
Two lines are parallel if they have the same slope.
Two lines are perpendicular if the product of their slopes is -1.
For a line with slope m, the slope of a perpendicular line is $-\frac{1}{m}$ (when m ≠ 0).
Special Cases
- A horizontal line has a slope of 0.
- A vertical line has an undefined slope (or infinite slope).
- A line with a positive slope rises from left to right.
- A line with a negative slope falls from left to right.