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Slope Calculator Information
What is Slope?
The slope of a line measures its steepness and direction. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line:
m = (y₂ - y₁) / (x₂ - x₁)
- m = slope
- (x₁, y₁) = first point on the line
- (x₂, y₂) = second point on the line
- m = slope
- (x₁, y₁) and (x₂, y₂) = two points on the line
Example: (1, 2) and (4, 6)
m = (6 - 2) / (4 - 1) = 4 / 3
m ≈ 1.33
m ≈ 1.33
Why Calculate Slope?
- Algebra & Geometry: Analyze lines, angles, and graphs.
- Construction: Design ramps, roofs, and roads.
- Physics: Study motion and velocity on graphs.
- Everyday Life: Calculate grade or incline for accessibility.
Tips for Accurate Calculation
- Use Consistent Units: All coordinates should use the same unit (e.g., meters, feet).
- Order Matters: Subtract in the same order for both numerator and denominator.
- Vertical Lines: If x₂ = x₁, the slope is undefined (vertical line).
Frequently Asked Questions (FAQ)
Q: What does a positive or negative slope mean?
A: Positive slope rises left to right; negative slope falls left to right.
Q: What if the slope is zero?
A: The line is horizontal.
Q: What if the slope is undefined?
A: The line is vertical (x₂ = x₁).
Q: Can I use decimals or fractions?
A: Yes, the calculator works with both.
Q: What is the equation of a line?
A: y = mx + b, where m is the slope and b is the y-intercept.