Slope

The slope of a line is a measure of how steep it is. It is often denoted by the letter "m." The slope of a line can be positive, negative, zero, or undefined.

Calculating Slope

To calculate the slope of a line, you can use the following formula:

\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]

Where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line. The slope formula represents the change in the y-coordinates divided by the change in the x-coordinates between two points on the line.

Interpreting Slope

If the slope is positive, it means the line is going uphill from left to right. If the slope is negative, it means the line is going downhill from left to right. A slope of zero indicates a horizontal line, and an undefined slope indicates a vertical line.

Study Guide

Here are some key points to remember when studying slope:

1. The slope of a line measures its steepness.
2. The slope formula is \(\frac{{y_2 - y_1}}{{x_2 - x_1}}\).
3. A positive slope means the line goes uphill, a negative slope means the line goes downhill, a zero slope means the line is horizontal, and an undefined slope means the line is vertical.
4. When finding the slope, always use the formula and substitute the coordinates of two points on the line.

Understanding slope is important in various mathematical concepts, such as graphing linear equations, calculating rates of change, and understanding the direction of a line. Practice using the slope formula with different sets of coordinates to reinforce your understanding.