Given a graph, can you think of two different ways to find the slope?
4
Practice makes perfect
We are given a graph and we want to find the slope of the line. To do it, let's first recall the Slope Formula.
The Slope Formula
The slope of a line that passes through the points (x_1,y_1) and (x_2,y_2) is given by the following formula.
slope = rise/run = y_2 - y_1/x_2-x_1, where x_2-x_1 ≠0
The x -coordinate we use first in the denominator must belong to the same ordered pair as the y -coordinate we use first in the numerator.
Observing the given graph, we can see that the line passes through the points (3,12) and (5,20).
One way to use a graph to find the slope of a line is to count the change in the x -coordinates and the change in the y-coordinates.
We can see that as the graph travels from left to right, the rise, or change in y, is 8. Similarly, the run, or change in x, is 2.
slope=rise/run ⇔ m=8/2=4
We can confirm this answer by using the other ratio from the Slope Formula.
slope = y_2 - y_1/x_2-x_1
We will use the given points to find for the slope.
