1. Bell Ringer April 04, 2014 School Day 145 Daily Decimal 1. What is the school day to the remaining days in the 2 nd Semester rounded to nearest tenth as a Percent. Homework: No Homework Clear Target – Students will apply the concept of slope and y-intercept in a real-world situation.

2. Directly & Inversely Proportional Today you will begin to learn about two different mathematical relationships: Directly proportional and Inversely proportional. You have already done some work with proportional relationships. Can anyone tell me something you already know about proportional relationships?

3. DIRECTLY PROPORTIONAL AND PROPORTIONAL MEAN THE SAME THING. If a relationship is directly proportional, two quantities increase or decrease at the same rate. For instance, in a directly proportional relationship, if you earn $5 for one hour of babysitting, you would earn $10 for two hours, $15 for three hours, etc. We could say y = 5x, where “x” = hours and “y” = amount of money you will make babysitting.

4. Composition Notebook Go to your Table of Contents Label page 74 “Directly/Inversely Proportional Graphs”

5. GraFun Activity Worksheet DO NOT WORK AHEAD To determine the “y” values, we will substitute each “x” value into the given expression in the middle column. Notice that in a directly proportional relationship, as the “x” values increase in the table, the “y” values are also increasing.

6. GraFun Activity Worksheet Now, we will see how a directly proportional relationship is represented on a graph. We will plot the ordered pairs from the table on the graph to see what type of line is shown. Notice that the line is straight and it passes through the origin if we extend the line in that direction. This is the way that a directly proportional relationship will ALWAYS look when shown on a graph.

7. GraFun Activity Worksheet What do you think it means in our babysitting scenario that the line passes through the origin? If no hours are worked, then no money is earned.

8. GraFun Activity Worksheet An inversely proportional relationship is much different from a directly proportional one. In an inversely proportional relationship, the “x” and “y” values of each ordered pair will produce the same number when multiplied together. OK, imagine this: You have to build a rectangular table that has an area of 20 square feet. What would the length and width of the table be? So an example of one table’s dimensions might be 4 feet by 5 feet.

9. GraFun Activity Worksheet Look at the worksheet again, at the bottom of the page there is another table. The lengths of the possible rectangular tables are listed in the input column (the “x” values) and the widths of the rectangular table will go in the output column (the “y” values). To determine the “y” values, we will substitute each “x” value into the given expression in the middle column.

10. GraFun Activity Worksheet Notice that as the “x” values increase in the table, the “y” values are decreasing. Now, we will see how an inversely proportional relationship is represented on a graph. We will plot the ordered pairs from the table on the graph to see what type of line is shown. Notice that the line is curved and it DOES NOT pass through the origin at all. This is the way that an inversely proportional relationship will ALWAYS look when shown on a graph.

11. GraFun Activity Worksheet Why do you think this line does not pass through the origin? What would that mean when you think about the rectangular table we have to make? If the length and width is zero, there would be no table. Do you think that the curved line on the graph would ever touch the x-axis or the y-axis if we extended it further? No, because you can’t have a table with no length and you can’t have a table with no length.

12. Before the quiz: Make sure you have: a sheet of paper calculator composition notebook You will have 15 minutes to complete this quiz.

13. After the quiz: When you are finished with quiz, place the quiz facedown on the counter and sit quietly until class is dismissed.