Slope Calculator
Calculate slope between two points with step-by-step solutions
Calculate Slope Between Two Points
First Point (x₁, y₁)
Second Point (x₂, y₂)
Visual Representation
Results
Slope (m)
Line Equation
Y-Intercept (b)
Angle with X-axis
Percentage Grade
Distance Between Points
Step-by-Step Solution
Point 2: (1, 1)
b = 0 - 0.000000 = 0.000000
Example Problems
Positive Slope Example
Points: (1, 2) and (3, 6)
Negative Slope Example
Points: (2, 8) and (4, 2)
Horizontal Line (Zero Slope)
Points: (1, 3) and (5, 3)
Vertical Line (Undefined Slope)
Points: (3, 1) and (3, 7)
Types of Slopes
Quick Reference
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Point-Slope Form
y - y₁ = m(x - x₁)
Slope-Intercept Form
y = mx + b
Angle Formula
θ = arctan(m)
Percentage Grade
Grade = m × 100%
Understanding Slope
What is Slope?
Slope is a measure of the steepness of a line. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line. The slope is constant for any straight line.
Slope Formula
The slope formula is derived from the definition of slope as rise over run:
Slope Interpretation
Positive Slope (m > 0)
The line rises from left to right. As x increases, y increases.
Negative Slope (m < 0)
The line falls from left to right. As x increases, y decreases.
Zero Slope (m = 0)
Horizontal line. y remains constant as x changes.
Undefined Slope
Vertical line. x remains constant as y changes.
Real-World Applications
Road Grade
The steepness of roads is measured as a percentage grade, which is slope × 100%.
Roof Pitch
Roof slope is crucial for water drainage and architectural design.
Rate of Change
In physics, slope represents velocity (position vs time) or acceleration.
Common Formulas
From Slope to Angle
θ = arctan(m)
Where θ is the angle in radians (multiply by 180/π for degrees)
Percentage Grade
Grade = slope × 100%
A 10% grade means a rise of 10 units for every 100 units horizontal