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Tables, and Graphs 3-5 Equations, Tables, and Graphs 3-5 Equations, Warm Up Problem of the Day Lesson Presentation Course Course 33 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 –3, 21, –33 2. y = 3.8x – 12 –12, 3.2, –31 3. y = 1.6x + 5.9 5.9, 12.3, –2.1 Course 3 3-5 Equations, Tables, and Graphs Problem of the Day You buy two fruit baskets. Each basket contains three bunches of bananas. Each bunch contains five bananas. How many bananas do you have? 30 Course 3 3-5 Equations, Tables, and Graphs Learn to generate different representations of the same data. Course 3 3-5 Equations, Tables, and Graphs 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 An equation shows how the variables are related. Course 3 Helpful Hint The number of seconds s is the input value. The depth d is the output value. 3-5 Equations, Tables, and Graphs Additional Example 1 Continued Graph Table s 0 1 2 3 h 0 12 24 36 A table identifies values that make the function true. Course 3 50 h 40 30 20 10 0 1 2 3 4 5 s A graph is a visual image of the values in the table. 3-5 Equations, Tables, and Graphs 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 An equation shows how the variables are related. Course 3 3-5 Equations, Tables, and Graphs Check It Out: Example 1 Continued Graph Table s 0 h 0 1 2 3 15 30 45 4 60 A table identifies values that make the function true. Course 3 h 75 60 45 30 15 0 1 2 3 4 5 s A graph is a visual image of the values in the table. 3-5 Equations, Tables, and Graphs Additional Example 2: Using Tables to Generate Different Representations of Data Use the table to make a graph and to write an equation. Course 3 x 0 1 2 y –1 0 1 3 2 Look for a pattern in the values: 0=1–1 1=2–1 2=3–1 Each value of y is the value of x minus 1. 3-5 Equations, Tables, and Graphs Additional Example 2 Continued Use the table to make a graph and to write an equation. y x 0 1 y –1 0 2 3 1 2 y=x–1 Course 3 4 2 x –4 –2 –2 –4 0 2 4 3-5 Equations, Tables, and Graphs Check It Out: Example 2 Use the table to make a graph and to write an equation. Course 3 x 0 1 2 y 3 4 5 3 6 Look for a pattern in the values: 4=1+3 5=2+3 6=3+3 Each value of y is the value of x plus 3. 3-5 Equations, Tables, and Graphs Check It Out: Example 2 Continued Use the table to make a graph and to write an equation. x 0 1 2 y 3 4 5 3 6 y=x+3 Course 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. d Look for a pattern in the values: 8 4 t –8 –4 –4 –8 Course 3 0 4 8 4=2 • 1+2 6=2 • 2+2 8=2 • 3+2 3-5 Equations, Tables, and Graphs Additional Example 3 Continued Use the graph to make a table and to write an equation. Each value of d is 2 times the value of t plus 2. Course 3 t 0 1 d 2 4 2 3 6 8 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. d Look for a pattern in the values: 8 4 t –4 –2 –4 –8 Course 3 0 2 4 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. Each value of d is t minus 1. t 0 1 2 3 Course 3 3 times the value of d –1 2 5 8 d = 3t – 1 3-5 Equations, Tables, and Graphs Lesson Quiz: Part I 1. Make a table and sketch the graph of w = –2x + 3. w Course 3 x 0 1 2 w 3 1 -1 3 -3 4 2 x –4 –2 –2 –4 0 2 4 3-5 Equations, Tables, and Graphs Lesson Quiz: Part II 2. Use the table to sketch a graph and write an equation. y = –x y x y -1 1 0 0 1 -1 2 Course 3 -2 4 2 x –4 –2 –2 –4 0 2 4 3-5 Equations, Tables, and Graphs Lesson Quiz: Part III 3. Use the graph to make a table and to write an equation. y = 4x + 1 x 2 1 0 y 9 5 1 –1 –3 Course 3