Slope Calculator
Find the slope between two points. Outputs slope, line equation in slope-intercept, point-slope, and standard forms with interactive graph.
Slope
Results update instantly as you type
Enter Values
Standard Form
-4x + 3y = 1
Distance Between Points
5
Y-Intercept
(0, 0.3333)
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Slope
1.3333
increasing (positive slope)
Interactive Line Plot
Slope-Intercept
y = 1.3333x + 0.3333
Point-Slope
y − 3 = 1.3333(x − 2)
Standard Form
-4x + 3y = 1
Y-Intercept
(0, 0.3333)
Distance
5
The Formula
The slope formula measures the rate of change between two points. Slope-intercept form (y = mx + b) shows the slope m and y-intercept b. Point-slope form is useful when you know one point and the slope. Standard form (Ax + By = C) is common for systems of equations.
Variable Definitions
Slope
The rate of change: rise over run. Positive means increasing, negative means decreasing, zero means horizontal, undefined means vertical.
Y-Intercept
The point where the line crosses the y-axis (x = 0). In slope-intercept form y = mx + b, b is the constant term.
Point 1
The first known point on the line. Used in the point-slope formula.
Point 2
The second known point on the line. The two points determine the line uniquely.
How to Use This Calculator
- 1
Enter the coordinates of two points (X₁, Y₁) and (X₂, Y₂) on the line.
- 2
View the slope as both a decimal and a simplified fraction (rise over run).
- 3
See all three equation forms: slope-intercept (y = mx + b), point-slope, and standard form (Ax + By = C).
- 4
The direction indicator tells you whether the line is increasing, decreasing, horizontal, or vertical.
- 5
Distance between the points and the y-intercept are also calculated automatically.
The slope of a line is the ratio of vertical change (rise) to horizontal change (run)
Understanding the Concept
The slope of a line measures its steepness and direction. A positive slope means the line rises from left to right; a negative slope means it falls. A zero slope is horizontal, and an undefined (infinite) slope is vertical. Slope is fundamental to calculus (derivatives measure the slope of a curve at any point), physics (velocity = slope of a distance-time graph), economics (marginal cost = slope of the cost function), and countless real-world applications. Slope-intercept form (y = mx + b) is the most intuitive — m tells you the steepness and b tells you where the line crosses the y-axis. Point-slope form (y − y₁ = m(x − x₁)) is useful when you know a point and the slope. Standard form (Ax + By = C) is convenient for finding both intercepts quickly and for solving systems of linear equations. The calculator also computes the distance between the two points using the Pythagorean theorem: d = √((x₂ − x₁)² + (y₂ − y₁)²). Real-world slope examples: a 6% road grade means the road rises 6 feet for every 100 feet of horizontal distance (slope = 0.06).
Frequently Asked Questions
Sources & References
Related Calculators
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