📈
Slope Calculator
Calculate slope between two points
Share Slope Calculation
📚 How to Use & Examples
⚡Quick Examples of Slope
📐Slope Formula
Slope=
y₂-y₁
x₂-x₁
Where (x₁, y₁) and (x₂, y₂) are two points on the line
🔍How to Calculate Slope
How to Calculate
Step 1: Identify your two points: (x₁, y₁) and (x₂, y₂)
Step 2: Calculate the change in y: y₂ - y₁
Step 3: Calculate the change in x: x₂ - x₁
Step 4: Divide change in y by change in x
Example: Points (1, 2) and (3, 8)
• Change in y = 8 - 2 = 6
• Change in x = 3 - 1 = 2
• Slope = 6 ÷ 2 = 3
Slope Interpretation
Positive slope: line rises from left to right
Negative slope: line falls from left to right
Zero slope: horizontal line
Special Cases
Vertical lines: have undefined slope (division by zero)
Horizontal lines: have zero slope
🌍Real-World Applications
🏗️ Construction
Roof pitch, ramp gradients, road grades
📊 Economics
Rate of change in prices, profit margins
⛷️ Sports
Ski slope steepness, running track banking
🚗 Engineering
Highway gradients, drainage systems
❓Frequently Asked Questions
What if x₁ equals x₂?
If x₁ = x₂, you have a vertical line, and the slope is undefined (division by zero). Vertical lines have no finite slope.
What does a slope of 1 mean?
A slope of 1 means for every 1 unit you move right, you move 1 unit up. This creates a 45° angle with the horizontal.
Can slope be a fraction?
Yes! A slope of 2/3 means for every 3 units right, you move 2 units up. Fractions are very common in slope calculations.
How do I remember the slope formula?
Remember 'rise over run': slope = (rise)/(run) = (change in y)/(change in x) = (y₂-y₁)/(x₂-x₁).
💡Calculator Tips & Best Practices
⚠️Watch for Vertical Lines
If x₁ = x₂, the slope is undefined because you'd divide by zero
💡Order Doesn't Matter
You can use either point as (x₁, y₁) - just be consistent with your order
⭐Check Your Signs
Pay careful attention to positive and negative coordinates when calculating
💡Visualize the Line
Try to picture the line in your head - does your slope make sense?
📚 References & Further Reading
Comprehensive coverage of coordinate geometry and slope calculations
External Link
Interactive lessons on slope and graphing linear equations
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.