Mathematical+Reflections+p.+36+0910

September 6, 2009 Block F Math Big Idea: Many real world situations can be modeled and predicted using mathematics Essential Question: How can I model a non-linear relationship?**
 * A.R.


 * Notes: An inverse relationship is a non-linear relationship in which the product of two variables is constant. In an inverse relationship, the values of one variable decrease as the other value increases. For example: The inverse relationship in the bridge-length experiment was the length and the breaking weight.**


 * __Mathematical Reflections Page 36__**


 * 1. What common patterns of change did you find in the tables and the graphs of these relationships? Did all three relationships fit the same pattern?**

I noticed that in all the tables and the graphs, they had non-linear relationships unlike the ones in Investigation 1. They did not fit the same pattern because they were non-linear. The three relationships all had the same pattern..


 * 2. How are the patterns in the tables and the graphs of these relationships different from the pattern in the tables and the graphs of the linear relationships you explored in Investigation 1?**

The patterns in the tables and the graphs of these relationships were different because these were non-linear lines. They did not have a constant rate of increase or decrease. The ones we explored in Investigation 1 were linear, so they had a constant rate of change.


 * 3. There are many types of non-linear relationships, some of which you will explore later this year. The type of relationship you studied in this investigation is called an inverse relationship. Can you think of some reasons this name is appropriate?**

I think that an inverse relationship is an appropriate way to call an inverse relationship is because the y value is doing the opposite of the x value.

In this investigation we learned about non-linear lines, graphs, tables and equations. If a line is straight, then it has no curves,and it is linear. If a line isn't straight, it is non-linear. These are examples of linear and non-linear tables:
 * Summary:**


 * __Linear__**


 * X || Y ||
 * 1 || 2 ||
 * 2 || 4 ||
 * 3 || 6 ||
 * 4 || 8 ||


 * __Non-Linear__**


 * X || Y ||
 * 1 || 7500 ||
 * 2 || 3750 ||
 * 3 || 2500 ||
 * 4 || 1875 ||