Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two common misperceptions of students when drawing the best-fit line are that the line should "hit" as many points as possible and that the line should divide the data set so that the number of points above and below the line is equal. It is difficult to counter these beliefs with mathematical reasoning when the mathematical process behind finding a line of best fit seems beyond the students' current knowledge. To develop insight into this process, the author uses the median-median line, which uses basic principles of coordinate geometry and linear equations to calculate the equation of the line of best fit. The process provides students with a way of thinking about the appropriate criteria to consider when drawing best-fit lines and reveals the mystery of what is happening in their calculator or computer when best-fit lines are generated. In addition, students are able to compare and contrast the median-median line and least-squares regression line and make decisions about which may be more appropriate for a given set of data. (Contains 7 figures.)