3-5 Equations, Tables, and Graphs

Warm UpFor 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

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

242

363

121

00

hs

Table

3-5 Equations, Tables, and Graphs

Additional Example 1 Continued

h 50

40

30

20

10

0 1 2 3 4 5 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

453

302

604

151

00

hs

Table

3-5 Equations, Tables, and Graphs

Check It Out: Example 1 Continued

h 75

60

45

30

15

0 1 2 3 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.

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 – 11 = 2 – 12 = 3 – 1

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 2 4

2

4

–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:

52

63

41

30

yx

Each value of y is the value of x plus 3.

4 = 1 + 35 = 2 + 36 = 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

52

63

41

30

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 = 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.

62

83

41

20

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

0–2–4 2 4

4

8

–4

–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.

52

83

21

–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

–12

–33

11

30

wx

x

w

0–2–4 2 4

2

4

–2

–4

3-5 Equations, Tables, and Graphs

2. Use the table to sketch a graph and write an equation.

Lesson Quiz: Part II

-11

-22

00

1-1

yx

x

y

0–2–4 2 4

2

4

–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

52

73

31

10

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 + 1 B. y = 2x – 1

Lesson Quiz for Student Response Systems