Identifying proportional relationships with graphs

The  exercise appears under the 7th grade (U.S.) Math Mission. This exercise explores the graphical representation of proportional relationships and direct variation.

Types of Problems
There are three types of problems in this exercise:


 * 1) Determine which graphs are direct variation: This problem provides a single coordinate axis with several graphs drawn. The student is asked to determine how many of the graphs represent a proportional relationship.Iprwg1.png
 * 2) Graph the points and determine if it is direct variation: This problem has a chart or other representation of several data points. The student is asked to graph the points on the graph and determine whether or not the data is in a proportional relationship.Iprwg2.png
 * 3) Determine which graphs show proportional relationships: This problem provides two graphs that may or may not represent proportional relationships. The student is asked to identify which, if either, of the graphs do indeed represent direct variation.Iprwg3.png

Strategies
Knowledge of direct variation, ratios, proportions and graphing linear equations are encouraged to ensure success on this exercise.
 * 1) A direct variation, or proportional relationship, can be represented by $$y=kx$$.
 * 2) The graph of a proportional relationship must be linear, and it must go through the origin.

Real-life Applications

 * 1) Several problems on this exercise are real-life applications.
 * 2) Rates provide a real-life application of proportional relationships and are used in chemistry and physics.