2. Linear Equations & Intercept Form Write a linear equation in intercept form given a recursion routine, a graph, or data Learn the meaning of y-intercept for a linear equation in intercept form

3. You have used recursive routines, graphs, and tables to model linear relationships. In this lesson you will write linear equations from recursive routines. There are many real world situations that can be represented by linear equations. Different physical activities cause people to burn calories at different rates. Let’s study one person’s workout data.

4. Working Out with Equations Do Now: 1. Please take a book-Page 178 and a Communicator. 2. Either copy the chart into your notebook or fill in the first column on my worksheet. 3. Write down one real life example where a recursive routine exist. For instance, where in real life situations do you “start” with a number and add a number each additional time?

5. Investigation Chart Manisha starts her exercise routine by jogging to the gym. Her trainer says this activity burns 215 calories. Her workout at the gym is to pedal a stationary bike. This activity burns 3.8 calories per minute. Pedaling time (min) X Total calories burned y 0215 1 2 20 30 45 60

6. Investigation Chart Work in your groups to complete steps 1-3. Be prepared to share your solutions with the rest of the class. Pedaling time (min) X Total calories burned y 0215 1 2 20 30 45 60

7. Questions to think about.. Whenever you see a table, there are always two questions to think about.. Where on the y-axis do you start? What number do you add each time? Pedaling time (min) X Total calories burned y 0215 1215 +___x 2 20215 +___x 30215 +___x 45215 +___x 60215 +___x

8. On the Graphing Calculator

9. Answer Key

10. Investigation Chart Let’s Complete steps 4-7 Together. (Communicator) Read page 179 Step 4. How can you write an expression for total calories burned after 20 minutes without using the calculator? Pedaling time (min) X Total calories burned y 0215 1 2 20 30 45 60

11. Step 6 Explanation Manisha’s linear relationship is shown by the equation: y = 215 + 3.8x or y = 3.8x + 215 This form y=a + bx is called the INTERCEPT FORM. The value of a is the y-intercept, which is the value of y when x = zero and the location where the graph crosses the y-axis. The number multiplied by x is b, which is called the coefficient of x.

12. CLASSWORK On Communicator

13. Step 8-page 179 Now let’s put these points into the graphing calculator. Do you remember how? We need to clear these screens and enter our new information. \ Now graph your equation to check that is passes through the points.

14. Step 8 Solution

15. Example A-Classwork Complete “part a” at your desk Sam’s Swim Swimming Time (min) Calories burned by Swimming Total Calories Burned 0 1 2 20 30 45 60 Suppose Sam has already burned 325 calories before he began to swim for his workout. His swim will burn 7.8 calories per minute. a.Create a table of values for the calories Sam will burn by swimming 60 minutes and the total calories he will burn after each minute of swimming.

16. Now try part b and c Sam’s Swim Swimming Time (min) Calories burned by Swimming Total Calories Burned 00325 17.8332.8 215.6340.6 20156481 30234559 45351676 60468793 Suppose Sam has already burned 325 calories before he began to swim for his workout. His swim will burn 7.8 calories per minute. b. Define variables and write an equation in intercept form to describe this relationship. c. On the same set of axes, graph the equation for total calories burned and the direct variation equation for the calories burned by swimming.

17. Example A Sam’s Swim Swimming Time (min) Calories burned by Swimming Total Calories Burned 00325 17.8332.8 215.6340.6 20156481 30234559 45351676 60468793 d.How are the graphs similar? How are they different? e.What are the different equations? f.What will different values of a in the equation y=a +bx do to the graph?

18. Example B page 181 A minivan is 220 miles from its destination, Flint. It begins traveling toward Flint at 72 mi/hr. a) Define variables and write an equation in intercept form for this relationship. b) Use your equation to calculate the location of the minivan after 2.5 hrs. c) Use your equation to calculate when the minivan will be 130 miles from Flint. d) Graph the relationship and locate the points that are the solutions to parts b and c. e) What is the real-world meaning of the rate of change in this relationship? What does the sign of the rate of change indicate?

19. Homework Finish class work and complete worksheet 3.4.