Rates and proportional relationships

The  exercise appears under the 8th Grade Math Mission. This exercise analyzes proportional rates in tables, graphs and equations.

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


 * 1) Select the equations that work: This problem provides a word problem and several possible equations. The student is asked to select all of the possibilities from the list that would satisfy the conditions written in the problem.Rapr1.png
 * 2) Tell which has faster or slower rate: This problem provides two proportional relationships in either context, graphs, tables or equations. The student is asked to select which relationship has either the faster or slower rate of change.Rapr2.png

Strategies
Knowledge of the multiple representations of functions would help with this exercise.
 * 1) A proportional relationship is of the form $$y=kx$$ for k a constant.
 * 2) The table form will always have a constant ratio when y is divided by x or vice versa.
 * 3) The graph will always be a line through the origin.
 * 4) The rate of proportionality (the k from the equation) is the slope of the line. The faster rate means the steeper (or greater) slope.