Connecting these points will form a straight line if the function is linear. Otherwise, we will have shown that the function is nonlinear.
Since we can use a straight edge to connect all of the given points, we know that they lie on the same line in the coordinate plane. This means that the function is linear.
Extra
Using the Rate of Change
We can also know if a function is linear by looking at the rate of change. A constant rate of change means that a function is linear. Rate of change tells us how many units a function moves up or down in comparison to how many units the function moves to the right. We usually call this the change in y over change in x or, more casually, the rise over run.
change iny/change inx=rise/run
Let's look at the given table to find the rate of change for this function.
Each time the value of x increases by 1, the value of y also increases by 1. This means that the rate of change is 1.
change iny/change inx=1/1=1
Because the rate of change is constantly 1 for every change in x, we know that our function is linear!
