In mathematics, slope is a number that tells us two things about a straight line: its steepness and its direction. Think of walking on a path. A steep path is hard to climb, while a flat path is easy. Slope measures exactly how steep that path is.

Every straight line has a slope. It's a fundamental property that helps us understand and compare different lines on a graph.

To find the slope, we look at how much a line goes up or down compared to how much it goes left or right. We call the vertical change the rise and the horizontal change the run.

Imagine you pick two points on a line. To get from the first point to the second, you might move up a certain amount (the rise) and over a certain amount (the run). The slope is simply the rise divided by the run.

This relationship is often written as a formula:

The rise tells us the change in the vertical direction (along the y-axis), and the run tells us the change in the horizontal direction (along the x-axis). Let's visualize this.

Lines can go in different directions, and the slope tells us which way. There are four possibilities.

When a line goes uphill, its rise is positive (you're going up) and its run is positive (you're moving to the right). A positive number divided by a positive number gives a positive slope.

A negative number (the rise) divided by a positive number (the run) results in a negative slope.

For a horizontal line, the rise is 0. Since $0$ divided by any non-zero number is $0$, the slope is zero.

For a vertical line, the run is 0. In math, we cannot divide by zero. Therefore, the slope of a vertical line is called undefined.

Understanding these four types of slope is key to describing and graphing linear equations.