Think about how these methods differ. In which case would we prefer one over the other?
See solution.
Practice makes perfect
We will begin by describing how to find the slope of a line by counting the units of vertical and horizontal change on the graph. Then, we will describe an example using the Slope Formula. Finally, we will compare both methods.
Counting Units of Vertical and Horizontal Change
In this method, we first count how many units of vertical and horizontal change there are from two points on a graph. Then, we will find the slope by taking the quotient between these changes.
However, we cannot do this if we do not have the graph at hand. Additionally, having the graph does not guarantee that this method can be used. There are cases in which counting will be impractical or imprecise because of the scale.
Using the Slope Formula
To find the slope m of a line using the Slope Formula, we need at least two points (x_1,y_1), (x_2,y_2) on a line.
m = y_2-y_1/x_2-x_1
The formula is also a good option if we have a tabular representation of the line with at least two points on it. For example, consider the following table.
x
y
2
4
3
6
4
8
Using the first two pair of values of the table, we can calculate the precise slope of the line. Let's do it!
