1. 10-2 Graphing Functions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 10-2 Graphing Functions Warm Up Write an equation for each function. Use your own variables. 1. The length of a wall is 4 ft more than three times the height. 2. The number of trading cards is 3 less than the number of buttons. l = 3h + 4 c = b – 3

3. 10-2 Graphing Functions Problem of the Day Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard? 30

4. 10-2 Graphing Functions MA.6.A.3.6 Construct and analyze tables, graphs, and equations to describe linear functions…using…algebraic notation. Also MA.6.A.3.2 Sunshine State Standards

5. 10-2 Graphing Functions Vocabulary linear equation

6. 10-2 Graphing Functions Additional Example 1: Finding Solutions of Equations with Two Variables Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4. Make a function table by using the given values for x to find values for y. 184(4) + 24 144(3) + 23 104(2) + 22 64(1) + 21 y4x + 2x Write these solutions as ordered pairs. (x, y) ‏ (1, 6) ‏ (2, 10) ‏ (3, 14) ‏ (4, 18) ‏

7. 10-2 Graphing Functions Check It Out: Example 1 Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4. 235(4) + 34 185(3) + 33 135(2) + 32 (x, y) 5x + 3x (2, 13) ‏ (3, 18) ‏ (4, 23) ‏ y

8. 10-2 Graphing Functions Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

9. 10-2 Graphing Functions Additional Example 2: Checking Solutions of Equations with Two Variables Determine whether the ordered pair is a solution to the given equation. (3, 21); y = 7x y = 7x Write the equation. 21 = 7(3) ‏ ? 21 = 21 ? Substitute 3 for x and 21 for y. So (3, 21) is a solution to y = 7x.

10. 10-2 Graphing Functions Check It Out: Example 2A Determine whether the ordered pair is a solution to the given equation. (4, 20); y = 5x y = 5x 20 = 5(4) ‏ ? 20 = 20 (4, 20) is a solution to y = 5x.

11. 10-2 Graphing Functions Check It Out: Example 2B Determine whether the ordered pair is a solution to the given equation. (2, 3); y = x + 1 y = x + 1 3 = 2 + 1 ? 3 = 3 (2, 3) is a solution to y = x + 1.

12. 10-2 Graphing Functions Check It Out: Example 2C Determine whether the ordered pair is a solution to the given equation. (6, 4); y = 2x - 7 y = 2 x – 7 4 = 2(6) - 7 ‏ ? 4 = 5 (6, 4) is not a solution to y = 2x - 7.

13. 10-2 Graphing Functions Check It Out: Example 2D Determine whether the ordered pair is a solution to the given equation. (5, 1); y = 3x - 12 y = 3x - 12 1 = 3(5) ‏ - 12 ? 1 = 3 (5, 1) is a solution to y = 3x - 12.

14. 10-2 Graphing Functions You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

15. 10-2 Graphing Functions Additional Example 3: Reading Solutions on Graphs Use the graph of the linear function to find the value of y for the given value of x. x = 4 When x = 4, y = 2. Start at the origin and move 4 units right. Move up until you reach the graph. Move left to find the y-value on the y-axis. The ordered pair is (4, 2). x y -4 -2 0 2 4 4 -2 -4 2

16. 10-2 Graphing Functions Check It Out: Example 3A For each graph of a linear function, find the values of y for the values of x given below the graph. x = 2 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 6

17. 10-2 Graphing Functions Check It Out: Example 3B For each graph of a linear function, find the values of y for the values of x given below the graph. x = 0 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 9

18. 10-2 Graphing Functions Check It Out: Example 3C For each graph of a linear function, find the values of y for the values of x given below the graph. x = 4 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 3

19. 10-2 Graphing Functions Check It Out: Example 3D For each graph of a linear function, find the values of y for the values of x given below the graph. x = 1 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 6

20. 10-2 Graphing Functions Check It Out: Example 3E For each graph of a linear function, find the values of y for the values of x given below the graph. x = 4 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 7

21. 10-2 Graphing Functions Check It Out: Example 3F For each graph of a linear function, find the values of y for the values of x given below the graph. x = 7 y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10 y = 8

22. 10-2 Graphing Functions Additional Example 4: Graphing Linear Functions Graph the function described by the equation. y = 3x+ 2 83(2) + 22 53(1) + 21 23(0) + 20 y3x + 2x (0, 2) ‏ (1, 5) ‏ (2, 8) ‏

23. 10-2 Graphing Functions Additional Example 4 Continued y 2 x 1 2 3 4 5 6 7 8 9 9 8 7 6 5 0 1 3 4

24. 10-2 Graphing Functions Check it out : Example 4A Graph the function described by the equation. y = x + 3 5(2) + 32 4(1) + 31 3(0) + 30 yx + 3x (0, 3) ‏ (1, 4) ‏ (2, 5) ‏

25. 10-2 Graphing Functions Check it out : Example 4A Continued y 2 x 1 2 3 4 5 6 7 8 9 9 8 7 6 5 0 1 3 4

26. 10-2 Graphing Functions Check it out : Example 4B Graph the function described by the equation. y = 2x + 5 92(2) + 52 72(1) + 51 52(0) + 50 y2x + 5x (0, 5) ‏ (1, 7) ‏ (2, 9) ‏ y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10

27. 10-2 Graphing Functions Check it out : Example 4C Graph the function described by the equation. y = 3x + 3 93(2) + 32 63(1) + 31 33(0) + 30 y3x + 3x (0, 3) ‏ (1, 6) ‏ (2, 9) ‏ y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10

28. 10-2 Graphing Functions Check it out : Example 4D Graph the function described by the equation. y = 8 - x 28 - 66 18 - 77 08 - 88 y8 - xx (8, 0) ‏ (7, 1) ‏ (6, 2) ‏ y 2 x 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 0 1 3 4 10

29. 10-2 Graphing Functions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

30. 10-2 Graphing Functions Lesson Quiz 1. Use the given x-values to write solutions as ordered pairs to the equation y = 10x + 5 for x = 0, 1, 2, and 3. 2. Determine whether (4, 2) is a solution to the equation y = 5x – 6. No, 2 ≠ 5(4) – 6 (0, 5), (1, 15), (2, 25), (3, 35 ‏ )

31. 10-2 Graphing Functions y 2 x 1 2 3 4 5 6 7 8 9 9 8 7 6 5 0 1 3 4 3. Graph the function described by the equation y = 5 – x. Lesson Quiz Cont.

32. 10-2 Graphing Functions 1. Use the given x-values to identify solutions as ordered pairs to the equation y = 7x + 4 for x = 1, 3, 5, and 7. Lesson Quiz for Student Response Systems

33. 10-2 Graphing Functions 2. Identify the graph of the function described by the equation y = x – 5. A. B. Lesson Quiz for Student Response Systems