1. Lesson 4-6 Pages 177-181 Functions and Linear Equations

2. What you will learn! How to graph linear equations.

3. Function Function table Domain Range Linear equation

4. What you really need to know! The solution of an equation with two variables consists of two numbers, one for each variable, that make the equation true. The solution is usually written as an ordered pair (x, y), which can be graphed.

5. What you really need to know! If the graph for an equation is a straight line, then the equation is a linear equation.

7. Example 1: Ann makes $6.00 an hour working at a grocery store. Make a function table that shows Ann’s total earnings for working 1, 2, 3, and 4 hours.

8. To solve this problem, we are going to make a table with: Input, Instructions, and Output.InputInstructionsOutput

9. Example 1:Input Function Rule Output Number of hours Multiply by 6 Total Earnings ($) 1 1 x 6 6 2 2 x 6 12 3 3 x 6 18 4 4 x 6 24 Domain Range Ann makes $6.00 an hour working at a grocery store. Make a function table that shows Ann’s total earnings for working 1, 2, 3, and 4 hours.

10. Example 2: Graph y = x + 3 x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 0 0 + 3 3 (0, 3) -1 + 3 2 (-1, 2)

11. (x, y) (2, 5) (1, 4) (0, 3) (-1, 2)

12. Example 3: Graph y = x – 3 x x – 3 y (x, y) 2 2 – 3 (2, -1) 1 1 – 3 -2 (1, -2) 0 0 – 3 -3 (0, -3) -1 – 3 -4 (-1, -4)

13. (x, y) (2, -1) (1, -2) (0, -3) (-1, -4)

14. Example 4: Graph y = -3x x-3xy (x, y) 2 -32 -6 (2, -6) 1 -31 -3 (1, -3) 0 -30 0 (0, 0) -3-1 3 (-1, 3)

15. (x, y) (2, -6) (1, -3) (0, 0) (-1, 3)

16. Example 5: Graph y = -3x + 2 x -3x + 2 y (x, y) 2 -32 + 2 -4 (2, -4) 1 -31 + 2 (1, -1) 0 -30 + 2 2 (0, 2) -3-1 + 2 5 (-1, 5)

17. (x, y) (2, -4) (1, -1) (0, 2) (-1, 5)

18. Example 6: Blue whales can reach a speed of 30 miles per hour in burst when in danger. The equation d = 30t describes the distance d that a whale traveling at that speed can travel in time t. Represent the function with a graph.

19. t30td (t, d) 1 30  1 30 (1, 30) 2 30  2 60 (2, 60) 3 30  3 90 (3, 90) 4 30  4 120 (4, 120) d = 30t Blue whales can reach a speed of 30 miles per hour in burst when in danger. The equation d = 30t describes the distance d that a whale traveling at that speed can travel in time t. Represent the function with a graph.

20. (t, d) (1, 30) (2, 60) (3, 90) (4, 120) (5, 150) (6, 180) 60 120 180 240 300 360 0 2 4 8 6 0

21. Page 179 Guided Practice #’s 3-7

22. 1 - 2 2 - 2 0 3 - 2 1 4 - 2 2 4-1 -4 4040 0 4141 4 4242 8

23. Pages 177-179 with someone at home and study examples! Read:

24. Homework: Page 180-181 #’s 8-20 even #’s 47-56 Lesson Check 4-6

25. 1 - 4-3 2 - 4-2 3 - 4 4 - 40 1 + 56 2 + 57 3 + 58 4 + 59 2-1-2 20200 21212 24 -6-16 -600 -61-6 -62-12 21-11 22-13 23-15 24-17 -2-1- 20 -20 - 2-2 -21 - 2-4 -22 - 2-6

28. Page 573 Lesson 4-6

29. Lesson Check 4-6