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**3-5 Warm Up Problem of the Day Lesson Presentation**

Equations, Tables, and Graphs Course 3 Warm Up Problem of the Day Lesson Presentation

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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

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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

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**Learn to generate different representations of the same data.**

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**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 An equation shows how the variables are related. The number of seconds s is the input value. The depth d is the output value. Helpful Hint

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**Additional Example 1 Continued**

Table Graph h 50 40 30 20 10 1 2 3 4 5 s s h 1 12 2 24 3 36 A table identifies values that make the function true. A graph is a visual image of the values in the table.

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**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 An equation shows how the variables are related.

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**Check It Out: Example 1 Continued**

Table Graph h 75 60 45 30 15 1 2 3 4 5 s s h 1 15 2 30 3 45 4 60 A table identifies values that make the function true. A graph is a visual image of the values in the table.

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**Additional Example 2: Using Tables to Generate Different Representations of Data**

Use the table to make a graph and to write an equation. x y –1 1 2 3 Look for a pattern in the values: 0 = 1 – 1 Each value of y is the value of x minus 1. 1 = 2 – 1 2 = 3 – 1

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**Additional Example 2 Continued**

Use the table to make a graph and to write an equation. x y –2 –4 2 4 x y –1 1 2 3 y = x – 1

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Check It Out: Example 2 Use the table to make a graph and to write an equation. x y 3 1 4 2 5 6 Look for a pattern in the values: 4 = 1 + 3 Each value of y is the value of x plus 3. 5 = 2 + 3 6 = 3 + 3

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**Check It Out: Example 2 Continued**

Use the table to make a graph and to write an equation. x y 3 1 4 2 5 6 y = x + 3

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**Use the graph to make a table and to write an equation.**

Additional Example 3: Using Graphs to Generate Different Representations of Data Use the graph to make a table and to write an equation. t d –4 –8 4 8 Look for a pattern in the values: 4 = 2 • 1 + 2 6 = 2 • 2 + 2 8 = 2 • 3 + 2

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**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. t d 2 1 4 6 3 8 d = 2t + 2

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**Use the graph to make a table and to write an equation.**

Check It Out: Example 3 Use the graph to make a table and to write an equation. t d –2 –4 2 4 8 –8 Look for a pattern in the values: 2 = 3 • 1 – 1 5 = 3 • 2 – 1 8 = 3 • 3 – 1

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**Check It Out: Example 3 Continued**

Use the graph to make a table and to write an equation. Each value of d is 3 times the value of t minus 1. t d –1 1 2 5 3 8 d = 3t – 1

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**1. Make a table and sketch the graph of w = –2x + 3. x w 3 1 2 -1 -3**

Lesson Quiz: Part I 1. Make a table and sketch the graph of w = –2x + 3. x w –2 –4 2 4 x w 3 1 2 -1 -3

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**2. Use the table to sketch a graph and write an equation. y = –x x y **

Lesson Quiz: Part II 2. Use the table to sketch a graph and write an equation. y = –x x y –2 –4 2 4 x y -1 1 2 -2

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Lesson Quiz: Part III 3. Use the graph to make a table and to write an equation. y = 4x + 1 x y 2 9 1 5 –1 –3

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