1. 3-5 Equations, Tables, and Graphs Warm Up For each function, find the value of y for x = 0, x = 4, and x = –5. 1. y = 6x – 3 2. y = 3.8x – 12 3. y = 1.6x + 5.9 –3, 21, –33 –12, 3.2, –31 5.9, 12.3, –2.1

2. 3-5 Equations, Tables, and Graphs Learn to generate different representations of the same data.

3. 3-5 Equations, Tables, and Graphs An equation shows how the variables are related. Additional Example 1: Using Equations to Generate Different Representations of Data The height h of an airplane s seconds from take-off is h = 12s. Make a table and sketch a graph of the equation. Equation h = 12s The number of seconds s is the input value. The depth d is the output value. Helpful Hint

4. 3-5 Equations, Tables, and Graphs A table identifies values that make the function true. Additional Example 1 Continued 242 363 121 00 hs Table

5. 3-5 Equations, Tables, and Graphs Additional Example 1 Continued h 50 40 30 20 10 012345 s A graph is a visual image of the values in the table. In this case, the graph is continuous, so draw a line through the points. Graph

6. 3-5 Equations, Tables, and Graphs An equation shows how the variables are related. Check It Out: Example 1 The height h of a helicopter s seconds from take-off is h = 15s. Make a table and sketch a graph of the equation. Equation h = 15s

7. 3-5 Equations, Tables, and Graphs A table identifies values that make the function true. Check It Out: Example 1 Continued 453 302 604 151 00 hs Table

8. 3-5 Equations, Tables, and Graphs Check It Out: Example 1 Continued h 75 60 45 30 15 0123 4 5 s Graph A graph is a visual image of the values in the table. In this case, the graph is continuous, so draw a line through the points.

9. 3-5 Equations, Tables, and Graphs Use the table to make a graph and to write an equation. Additional Example 2: Using Tables to Generate Different Representations of Data Look for a pattern in the values: 12 23 01 –10 yx Each value of y is the value of x minus 1. 0 = 1 – 1 1 = 2 – 1 2 = 3 – 1

10. 3-5 Equations, Tables, and Graphs Use the table to make a graph and to write an equation. Additional Example 2 Continued 12 23 01 –10 yx x y 0 –2 –4 24 2 4 –2 –4 y = x – 1

11. 3-5 Equations, Tables, and Graphs Use the table to make a graph and to write an equation. Check It Out: Example 2 Look for a pattern in the values: 52 63 41 30 yx Each value of y is the value of x plus 3. 4 = 1 + 3 5 = 2 + 3 6 = 3 + 3

12. 3-5 Equations, Tables, and Graphs Use the table to make a graph and to write an equation. Check It Out: Example 2 Continued 52 63 41 30 yx y = x + 3

13. 3-5 Equations, Tables, and Graphs Additional Example 3: Using Graphs to Generate Different Representations of Data Use the graph to make a table and to write an equation. Look for a pattern in the values: 4 = 2 1 + 2 6 = 2 2 + 2 8 = 2 3 + 2

14. 3-5 Equations, Tables, and Graphs Additional Example 3 Continued Use the graph to make a table and to write an equation. 62 83 41 20 dt Each value of d is 2 times the value of t plus 2. d = 2t + 2

15. 3-5 Equations, Tables, and Graphs Check It Out: Example 3 Use the graph to make a table and to write an equation. t d 0 –2 –4 24 4 8 –8 Look for a pattern in the values: 2 = 3 1 – 1 5 = 3 2 – 1 8 = 3 3 – 1

16. 3-5 Equations, Tables, and Graphs Check It Out: Example 3 Continued Use the graph to make a table and to write an equation. 52 83 21 –10 dt Each value of d is 3 times the value of t minus 1. d = 3t – 1

17. 3-5 Equations, Tables, and Graphs Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

18. 3-5 Equations, Tables, and Graphs 1. Make a table and sketch the graph of w = –2x + 3. Lesson Quiz: Part I –1 2 –3–33 11 30 wx x w 0 –2 –4 24 2 4 –2 –4

19. 3-5 Equations, Tables, and Graphs 2. Use the table to sketch a graph and write an equation. Lesson Quiz: Part II 1 -22 00 1 yx x y 0 –2 –4 24 2 4 –2 –4 y = –x

20. 3-5 Equations, Tables, and Graphs 3. Use the graph to make a table and to write an equation. Lesson Quiz: Part III 52 73 31 10 yx y = 2x + 1

21. 3-5 Equations, Tables, and Graphs 1.Identify the correct table and the corresponding graph of y = –3x + 2. A. B. Lesson Quiz for Student Response Systems

22. 3-5 Equations, Tables, and Graphs 2.Use the table to identify the graph and the equation. A.y = 2x B. y = –2x Lesson Quiz for Student Response Systems

23. 3-5 Equations, Tables, and Graphs 3.Use the graph to identify the table and the equation. A.y = 2x + 1B. y = 2x – 1 Lesson Quiz for Student Response Systems