Comparing linear functions

The  exercise appears under the 8th Grade Math Mission. This exercise finds points of comparison between various linear functions.

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


 * 1) Determine which function is changing faster: This problem provides two functions in different forms. The student is asked to determine which is increasing or decreasing faster.Clf1.png
 * 2) Find the line with the same slope: This problem provides a graph with several lines. The student is asked to determine which graph has the same slope as the given function.Clf2.png
 * 3) Figure out which function gets to a value faster: Instead of looking for a slope, this problem asks which function arrives at a certain output faster. The student selects the correct answer from a multiple choice list.Clf3.png
 * 4) Determine all lines that increase faster: This problem is much like another problem, but in this case there is a multiple select list to provide the possibility that more than one function would work.Clf4.png
 * 5) Determine information about intercepts: This problem provides two functions in different forms. The student is asked to determine which has the larger intercept.Clf5.png

Strategies
Knowledge of the various forms of lines and many forms of functions are a great advantage to doing this exercise accurately and efficiently.
 * 1) Knowing how to interpret slope and intercepts from graphs, charts and rules are a great advantage for speed.
 * 2) Problems could change decreasing for increasing and higher for lower in the future, so it is important to read carefully before answering.

Real-life applications

 * 1) Lines have many applications in business and the sciences.
 * 2) Intercepts tend to be initial conditions, and slope is the marginal cost to create more items.