Slope of a Line
The slope of a line is its angle, or steepness. A horizontal line (-----) has a slope of 0, and as the slope gets bigger the line gets steeper until it becomes a vertical line, which has no slope, or, more precisely, an undefined slope. The graph below has a slope of 0, which means that it has no steepness (it's flat!).
This next graph has a slope of 1:
You may be curious how we determine what the slope is, however. A slope is the change in y over the change in x. That means that is you had two points in a line, (0,0) and (2,2), the slope could be calculated like this:
The idea is that you put the amount that y changes between two points over the amount x changes between those same two points. Make sure to do the subtraction in the same order each time though. With the two points (1,3) and (4, 9), you must do 9-3 over 4-1 or 3-9 over 1-4. Given any two points, (x1,y1) and (x2, y2), the slope m is (y1-y2)/(x1-x2) or (y2-y1)/(x2-x1).
Now that we know how to calculate a slope, we must figure out how to graph the line. A line is often written in slope-intercept form, y = mx + b where m is the slope and b is the y-intercept. The y-intercept is the point where the line intersects the y-axis. If you are given y = 2x + 0, then the line has slope 2 and a y-int. of 0. Since the y-int. is 0, we know one point, (0,0). Because the slope is 2, or 2/1, we have to go up 2 for every 1 we go right. The line looks like this:
As you can see, the line goes up 2 points for every 1 points it goes right, meaning that the change in y is 2 when the change in x is 1. Slope = 2. For more information, please view our lesson on graphing lines.
