Slope measures the steepness of a line. It's measured as the ratio of the amount of horizontal change to the amount of vertical change, or "Rise over Run." You can use a graph to find slope by counting spaces to find the rise and run.
There are 4 different types of slope based on the direction of the line. Check out the intro to slope lesson to learn more about each type.
You can use a graph to find the slope of a line, but it's possible to find the slope without one. If you're given two points that are on the line, there is a formula that you can use to find the slope of the line. You can always pull out graph paper to find the slope, but you may find that the formula for slope can be faster and easier.
Here's the formula for the slope of a line:
Remember, slope is "Rise over Run." On a graph when you find the rise, you're finding the vertical change. Subtracting the y-coordinates will give you the Rise without needing a graph. Subtracting the x-coordinates will give you the amount of horizontal change, the Run. When you use the formula, make sure to subtract the y-values in the numerator and subtract the x-values in the denominator. It doesn't matter which point you call Point 1 or Point 2 as long as you subtract in the same order at each step.
When using the formula, follow the steps below: Step 1: Label the points. Step 2: Plug the values into the formula. Step 3: Write the slope as a simplified fraction.
Example 1 Find the slope of the line through the points (2,5) and (4,8).
Step 1: Label the points. It doesn't matter which one you pick as "Point 1" and "Point 2." Remember the x's are listed first in an ordered pair and the y's are listed second.
Step 2: Plug in the values. Subtract the y's on the top, subtract the x's on the bottom. Make sure to subtract in the same order in the numerator and denominator.
Step 3: Make sure your answer is simplified. 3/2 cannot be reduced, so we leave the answer as 3/2.
Example 2 Find the slope of a line through the points (-5,6) and (7,2).
Step 1: Label the points. Remember the x's are always listed first in the ordered pairs and the y's are listed second in each ordered pair.
Step 2: Plug the values into the formula. Make sure to subtract the y's in the numerator and subtract the x's in the same order for the denominator. Be especially careful when dealing with negative numbers. 7 minus a negative 5 is the same as 7 plus a positive 5.
Step 3: Make sure your answer is simplified. In this case, we can divide the numerator and denominator by 4 to simplify the answer.
It does not matter if you put the negative sign out in front of the fraction or if you leave it in the numerator.