Slope of a line

The slope of a line determines how steep the line is. In the standard equation of a line, y = mx + b, the slope is m. It is also commonly described as "rise over run" which tells us how much the y-value changes as the x-value changes.

Positive and negative slope

If the slope of a line is positive, the line increases (goes up) as it moves from left to right. If the slope of a line is negative, the line decreases (goes down) as it moves from left to right. Below are two lines where the only difference is that one slope is positive and the other is negative.

positive slope

negative slope

When the slope is 0, the line is a horizontal line that passes through the y-intercept. The slope of a vertical line is undefined since there is 0 horizontal change, so

Finding the slope from a graph

Given the graph of any line, it is possible to find the slope of the line by choosing two points on the line. The simplest way to do this is to pick 2 points on the line at integer coordinates then count the change in x and the change in y.

In the graph above, we can see that for every 2 units change in x, there is a 1 unit change in y, so the slope of the line is m = . It also intersects the y-axis at the point (0, 2), so the y-intercept is 2. Since we know both the slope and the y-intercept, we can find the equation of the graph: