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 – y = 1.6x –3, 21, –33 –12, 3.2, –31 5.9, 12.3, –2.1

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

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

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

3-5 Equations, Tables, and Graphs Additional Example 1 Continued h 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

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

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

3-5 Equations, Tables, and Graphs Check It Out: Example 1 Continued h 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.

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: –10 yx Each value of y is the value of x minus 1. 0 = 1 – 1 1 = 2 – 1 2 = 3 – 1

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

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: yx Each value of y is the value of x plus 3. 4 = = = 3 + 3

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

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 = = =

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

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 – –8 Look for a pattern in the values: 2 = 3 1 – 1 5 = 3 2 – 1 8 = 3 3 – 1

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

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

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– wx x w 0 –2 – –2 –4

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

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

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

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

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