In this section we use r to denote the value of the linear correlation coefficient. why do we refer to this correlation coefficient as being linear?

The r correlation coefficient is usually used in a conjunction with a best-fit line. This means that given a set of data points, we want to find a line which all the points are closest to. Then we measure how close the points are to the line using the r-value, which tells us the relationship between the variables. This correlation coefficient is called linear because the best-fit model we attempt to place is usually a line.