What is Slope?
Slope measures the steepness of a line. It tells you how much the line goes up or down (rise) for each step to the right (run).
The Slope Formula
Slope Formula: m = (y₂ - y₁)/(x₂ - x₁)
where (x₁,y₁) is the first point and (x₂,y₂) is the second point.
This is also known as "rise over run":
- Rise = Change in y = (y₂ - y₁)
- Run = Change in x = (x₂ - x₁)
How to Find Slope in 3 Easy Steps
- Find the rise: Subtract the y-coordinates (y₂ - y₁)
- Find the run: Subtract the x-coordinates (x₂ - x₁)
- Divide: Divide rise by run to get the slope
Understanding Slope Values
- Positive Slope: Line goes up from left to right
- Negative Slope: Line goes down from left to right
- Zero Slope: Horizontal line
- Undefined Slope: Vertical line (when run = 0)
Common Questions About Slope
What does slope mean in real life?
Slope has many real-world applications, such as:
- The grade (steepness) of a road or ramp
- The rate of change in pricing
- The incline of a roof or stairs
- The speed of an object (distance over time)
Why is slope called "rise over run"?
"Rise over run" is a simple way to remember that slope measures vertical change (rise) divided by horizontal change (run). It helps visualize what the slope represents.
What is a slope of 1?
A slope of 1 means the line rises one unit for every one unit it runs to the right. This creates a 45-degree angle with the x-axis.