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Slope Formula:
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The rise over run formula calculates the slope (m) of a line by dividing the vertical change (rise) by the horizontal change (run) between two points. It represents the steepness and direction of a line in coordinate geometry.
The calculator uses the slope formula:
Where:
Explanation: The slope indicates how much the vertical coordinate changes for each unit of horizontal change. A positive slope means the line rises as it moves right, while a negative slope means it falls.
Details: Slope calculation is fundamental in mathematics, engineering, architecture, and physics. It's used to determine angles of inclination, design ramps and roads, analyze graphs, and solve various real-world problems involving rates of change.
Tips: Enter the vertical change (rise) and horizontal change (run) in consistent units. The run must be a non-zero value. The result is a unitless value representing the slope.
Q1: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line with no vertical change as the horizontal position changes.
Q2: What is an undefined slope?
A: An undefined slope occurs when the run is zero, resulting in a vertical line where there's horizontal change without vertical change.
Q3: How is slope related to angle?
A: The slope is equal to the tangent of the angle of inclination: \( m = \tan(\theta) \), where θ is the angle between the line and the positive x-axis.
Q4: Can slope be negative?
A: Yes, a negative slope indicates that the line decreases (falls) as it moves from left to right.
Q5: How is slope used in real-world applications?
A: Slope is used in construction for ramp design, in civil engineering for road grading, in physics for velocity calculations, and in economics for rate-of-change analysis.