1. Rate of Change Slope Scenarios

2. Please pick up your calculator as you walk in! Identify the slope and y-intercept for each of the following equations. 1.y = 6x + 4 2.y = 7/4x – 5 3.2y = 4x – 2 4.4y – 16 = 8x Warm – Up!!

3. Scenario 1: Money in the Bank Let’s say that you have $100 saved up in your bank account. Then, you get a job working at the ice-cream shop. The owner tells you that you will make $40 a week. You decide to put all of your earnings right into your savings account. Answer the following questions. 1. What was the INITIAL amount in the account? 2. What is the RATE at which the account is increasing?

4. Scenario 1 Continued Week123456 Money Saved 100 a.What is the y – intercept? b.What is the slope (m)? c.What is the equation of the line?

5. Linear relationships are found in MANY real world examples whenever something is changing at a constant rate. When looking at real world examples in slope-intercept form…. y= mx +b y = Rate x + Initial

6. Scenario 2: The Fat Ferret Declan has been feeding his pet ferret, Mikey, way too much. One day, Declan decides to weigh him and he finds that Mikey is 14 pounds! Declan puts him on a strict diet. Since then, Mikey has been losing 2 pounds every month. MonthMikey’s Weight (lbs.) 0 1 2 3

7. Scenario 2 Continued a.What is the y – intercept? a.What is the slope (m)? a.What is the equation of the line? a.What is Mikey’s weight after 5 months? a.Will this relationship eventually stop?

8. Scenario 3: Cabarrus County Fair Ms. Hahn decided to spend the day at the Cabarrus County Fair. She paid the entrance fee into the fair, which was $10.00. Each ride she went on cost $2.50. Number of RidesMoney Spent 0 1 2

9. Scenario 3 Continued Write the equation that models Ms. Hahn’s day at the fair. If she goes on 7 rides and spent no money on food, how much did she spend?

10. Scenario 4: Save the Manatees In 2007, there were 28 manatees populating a specific stretch of water on the coast of Florida. Unfortunately, every year 4 pass away. Years since 2007Manatees 0 1 2 3 4

11. Scenario 4 Continued Write the equation that models the manatee population. In what year will this population be 0?

12. Practice Problems Given each of the following mini-scenarios, write a linear equation that models it. a.) The cost of using a cleaning company that charges a flat fee of $40 plus $15 per hour. b.) The height of a tree that is 88 ft. tall and grows at rate of 3 in. per year. c.) The number of cookies in a cookie jar starts if it starts with 49 cookies, but 7 are eaten every day. d.) The cell phone bill amount if it costs $44.50 plus $0.40 per minute. e.) Your test grades if they start at 100 but go down by 10 points per hour spent playing video games.