Slope Notes

Slope describes the steepness and direction of a line on a graph. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

1. **Understanding Rise and Run:**

The "rise" represents the vertical distance between two points on a line, and the "run" represents the horizontal distance between the same two points. A positive rise indicates an upward slope, while a negative rise indicates a downward slope. The slope is always calculated as rise/run.

2. **Calculating Slope:**

The slope (m) of a line passing through points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1). This formula helps determine the steepness of the line numerically. A larger absolute value of the slope indicates a steeper line.

3. **Interpreting Slope:**

A positive slope indicates a line that rises from left to right, while a negative slope indicates a line that falls from left to right. A slope of zero represents a horizontal line, and an undefined slope represents a vertical line. Understanding the sign and magnitude of the slope provides valuable information about the line's characteristics.

4. **Real-World Applications:**

Slope has numerous real-world applications, including calculating the grade of a road, determining the steepness of a roof, and analyzing the rate of change in various situations. Understanding slope is crucial for solving problems related to speed, distance, and time.

• **Conclusion**

Slope is a fundamental concept in mathematics that describes the steepness and direction of a line. It is calculated using the rise over run formula and can be interpreted to understand the line's characteristics and applied to vario

us real-world scenarios.