Slope Calculator
Slope is rise over run, (y₂ − y₁)/(x₂ − x₁): the line through (1, 2) and (4, 8) has slope m = 2.
2
- Rise ÷ run
- 6 ÷ 3
- Angle with the x-axis
- 63.43494882 °
- Line through both points
- y = 2x
- Direction
- rising (positive slope)
Step-by-step solution
- m = (y₂ − y₁) ÷ (x₂ − x₁)
- = (8 − 2) ÷ (4 − 1) = 6 ÷ 3
- m = 2
Slope Formula
m = (y₂ − y₁) ÷ (x₂ − x₁)
rise over run between points (x₁, y₁) and (x₂, y₂)
Worked Example
The line through (1, 2) and (4, 8):
- m = (y₂ − y₁) ÷ (x₂ − x₁)
- = (8 − 2) ÷ (4 − 1) = 6 ÷ 3
- m = 2
Angle with the x-axis: 63.43494882 ° · Line through both points: y = 2x · Direction: rising (positive slope)
Test-day tip
On the digital SAT, type the two points into the built-in graphing calculator as a table or plot them, then click the line: it shows the slope directly. For grid-in answers, enter the fraction (2/3) rather than a rounded decimal.
More Algebra Calculators
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Slope-Intercept Form Calculator
y = mx + b
m slope, b y-intercept = y₁ − m·x₁
Example: The line through (1, 2) and (4, 8): Slope-intercept form: y = 2x.
-
Point-Slope Form Calculator
y − y₁ = m(x − x₁)
point (x₁, y₁), slope m
Example: The line through (1, 2) with slope 3: Point-slope form: y − 2 = 3(x − 1).
-
Systems of Equations Calculator
a₁x + b₁y = c₁, a₂x + b₂y = c₂
solved by elimination / Cramer’s rule; determinant 0 means no unique solution
Example: The system 2x + 3y = 12 and x − y = 1: Solution: x = 3, y = 2.
-
Linear Inequality Calculator
ax + b < c → x < (c − b)/a
the inequality sign reverses when dividing by a negative a
Example: The inequality −3x + 4 < 10: Solution = x > -2.
Frequently asked questions
What does a slope of zero or undefined mean?
A slope of 0 is a horizontal line (y = constant). An undefined slope is a vertical line (x = constant), because the run x₂ − x₁ is zero.
How are the slopes of parallel and perpendicular lines related?
Parallel lines have equal slopes. Perpendicular lines have slopes that multiply to −1, so a line with slope 2 is perpendicular to one with slope −1/2.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Slope Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/slope-calculator/
IEEE
Scientific Converters, "Slope Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/slope-calculator/