ABSTRACT
Graphing ratios on the Cartesian coordinate plane is often overlooked as a visual representation that enables students to develop a fundamental understanding of how they might compare slopes, determine which equations are greater than others, and use the graphs to identify shared regions versus regions that are greater than or less than those shared regions. Comparing proportional relationships is often taught through cross multiplication or comparing common denominators. Students who are taught to examine double number lines as a representation for proportional relationships, or to graph those relationships on the Cartesian coordinate plane, are exposed to the foundational concept on which slope as ratio is built. Because the slope in an equation is a ratio, it is important that students recognize that they can graph multiple slopes on one set of axes and use the graph to decide how to shade in the appropriate regions.
