Slope of a Line
This topic looks at the math behind calculating the slope of a line you would find on a graph. Recall from the booklet that the formula for slope is:
The trouble that most students have is HOW you go about finding the values for the rise and the run of a line. This will be shown below.
Example
Find the slope of the following line, and tell what the slope represents.
Solution
We will start this backwards! First, let's tell what the slope represents. You can always tell what the slope represents from a graph by saying "The slope represents the dependent variable (the variable on the vertical axis) PER the independent variable (the variable on the horizontal axis)." So for this example we would say:
The slope represents cost PER person.
Now to find the value of the slope, we must first pick two points on the graph. These can be ANY two points that fall on the line, but it is easiest to pick points that fall right at a 'grid intersection'. The two points we will pick for this example will be at 20 people ($100) and 60 people ($300), as shown below:
The rise represents the amount that we have to rise to get from the first point (the lower point) to the higher point. The run is the distance we have to travel to get from the leftmost point to the rightmost point. These are animated below. (You may have to wait for the animation to start again.)
As you can see, the rise goes from $100 to $300. This is a 'distance' of $200. Therefore the rise is 200. The run goes from 20 people to 60 people. Therefore the run is 40. Now we can use the formula. Your work should look like:
And since we previously determined that the slope represents the cost per person, we know that the slope means that this line represents $5 per person.