What are some of the possible values for the slope of a line that lies in the shaded region? How do you know?
Students must both recognize that the lines must be of the form y=mx (the y-intercept value is 0), and that the slope of the line is between 0 and 1.
In addition to assessing students’ understanding of graphing, this question assesses students’ object conception of function. In order to characterize the properties of lines that pass through the shaded region, students must have a holistic understanding of the properties of lines as objects, rather than lines as a set of points. See also Connecting graphs to algebraic relationship and Action/Process/Object Concept of Function.