1. Relations and Functions Lesson 4: Properties of Linear Relations

2. Todays Objectives  Graph a set of data and determine the restrictions on the domain and range  Sort a set of graphs as functions and non-functions

3. Properties of Linear Relations  Before we start, work with a partner to complete A - C in the Try This activity on page 301. You can use the grid paper on your handout.

4. Solutions Width (units) Area (cm 2 ) 12 26 312 420 530 642 Width (units) Perimeter (units) 16 210 314 418 522 626 Non-linear (points not a straight line ) Linear (points in a straight line) Linear : means a graph has points that connect in a straight line or a graph is a straight line

5. Linear Relations  The cost for a car rental is $60, plus $20 for every 100 km driven. The independent variable is the distance driven and the dependent variable is the cost.  There are many different ways that we can identify that this is a linear relation:  Table of values  Set of ordered pairs  Graph

6. Identifying Linear Relations: Table of Values Distance (km)Cost ($) 0 60 100 80 200 100 300 120 400 140 Constant difference in independent and dependent variable = linear relation For a linear relation, a constant change in the independent variable results in a constant change in the dependent variable.

7. Identifying Linear Relations: Set of Ordered Pairs

8. Identifying Linear Relations: Graph Car Rental Cost Cost ($) Distance (km)

9. Rate of Change  The rate of change is $0.20/km ; that is, for each additional 1 km driven, the rental cost will increase by 20 cents. The rate of change is constant for a linear relation.  In any equation of the form y = mx + b, we can determine the rate of change by looking at the value of m. For example, an equation for this relation could be C = 0.20d + 60, where:  C is the dependent variable, cost  d is the independent variable, distance,  60 is the initial amount, and 0.20 is the rate of change (slope)

10. Example (You do)  Graph each equation and state whether or not it is linear  A) y = -3x + 25  B) y = 2x 2 + 5 xy -2 31 28 0 25 1 22 2 19 xy -2 13 7 0 5 1 7 2 13

11. Solutions AB LinearNon-linear

12. Example  A water tank on a farm holds 6000 L. Graph A represents the tank being filled at a constant rate. Graph B represents the tank being emptied at a constant rate. Graph A: Filling the tank Volume (L) Time (min) a)What is the independent /dependent variable? b)What is the rate of change?

13. Example

14. Example: You do a)What is the independent /dependent variable? b)What is the rate of change? Volume (L) Time (min) Graph B: Emptying the Tank

15. Example

16. Homework  Pg. 308-310  #3,5,7,9,11,13,15,17,19,22  Chapter 5 Vocab Quiz – Next Wednesday (may include any words from handouts)  Provincial Exam Practice – Next Friday  Chapter 5 Test – Tuesday, March 19

17. Wall Quiz  In teams of 3, move around the classroom and answer the questions posted on the walls  After the time runs out, return to your seats and we will compare answers  The team(s) with the most correct answers will win candy!