In option A we are told that a relationship is linear when the y-values change with respect to x at a constant rate. Let's look at an example.
As we can see, the y-values change with respect to x at a constant rate. This means that the rate of change is constant! Recall that the graph of a relationship with a constant rate of change is a straight line.
Therefore, if the points of a scatter plot have y-values that change with respect to x at a constant rate, the relationship is linear. We will definitely select option A as our answer. However, let's consider the other options.
Other Rates of Change
In the other options, y-values change with respect to x at a varying, increasing, and decreasing rates. Let's look at a few examples.
Notice that the best fit for the increasing and decreasing rate is a curved line. Also, when the rate at which y-values change with respect to x is varying, there is no association at all!
This means that none of these relationships are linear. Therefore, we will select only option A as our answer.
