Evaluate the slope of the line and compare it to the value of tan 225^(∘).
See solution.
Practice makes perfect
We are asked to show that the slope of the line at 225^(∘) from the x-axis is equal to the tangent of 225^(∘). Observing the given graph, we can see that the line passes through the points (1,1) and (2,2). One way to use a graph to find the slope of a line is to count out the change in x and y.
We can see that as the graph travels from left to right, the rise, or change in y, is 1. Similarly, the run, or change in x, is 1.
slope=rise/run ⇔ m=1/1=1
Next we will use the calculator to find the tangent of 225^(∘).
tan 225^(∘)=1
As we can see, tan 225^(∘) is also equal to 1. Therefore, the slope of a line at 225^(∘) from the x-axis is equal to the tangent of 225^(∘).
