10-2 Graphing Functions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

10-2 Graphing Functions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpWrite an equation for each function. Use your own variables.

1. The length of a wall is 4 ft more than three times the height.

2. The number of trading cards is 3 less than the number of buttons.

l = 3h + 4

c = b – 3


Problem of the Day

Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard?30


MA.6.A.3.6 Construct and analyze tables, graphs, and equations to describe linear functions…using…algebraic notation.

Also MA.6.A.3.2

Sunshine State Standards


Vocabulary

linear equation

10-2 Graphing Functions Additional Example 1: Finding Solutions of

Equations with Two Variables

Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.Make a function table by using the given values for x to find values for y.

184(4) + 24

144(3) + 23

104(2) + 22

64(1) + 21

y4x + 2x Write these solutions as ordered pairs.

(x, y)

(1, 6)

(2, 10)(3, 14)(4, 18)


Check It Out: Example 1

Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.

235(4) + 34

185(3) + 33

135(2) + 32

(x, y)5x + 3x

(2, 13)

(3, 18)

(4, 23)

y


Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.


Additional Example 2: Checking Solutions of Equations with Two Variables

Determine whether the ordered pair is a solution to the given equation.

(3, 21); y = 7x

y = 7x Write the equation.

21 = 7(3)?

21 = 21?

Substitute 3 for x and 21 for y.

So (3, 21) is a solution to y = 7x.


Check It Out: Example 2A


(4, 20); y = 5x

y = 5x

20 = 5(4)?

20 = 20

(4, 20) is a solution to y = 5x.


Check It Out: Example 2B


(2, 3); y = x + 1

y = x + 1

3 = 2 + 1?

3 = 3

(2, 3) is a solution to y = x + 1.


Check It Out: Example 2C


(6, 4); y = 2x - 7

y = 2 x – 7

4 = 2(6) - 7?

4 = 5

(6, 4) is not a solution to y = 2x - 7.


Check It Out: Example 2D


(5, 1); y = 3x - 12

y = 3x - 12

1 = 3(5) - 12 ?

1 = 3

(5, 1) is a solution to y = 3x - 12.


You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.


Additional Example 3: Reading Solutions on Graphs

Use the graph of the linear function to find the value of y for the given value of x.

x = 4

When x = 4, y = 2.

Start at the origin and move 4 units right.

Move up until you reach the graph. Move left to find the y-value on the y-axis.

The ordered pair is (4, 2).

x

y

-4 -2 0 2 4

4

-2

-4

2


Check It Out: Example 3AFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 2

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 6


Check It Out: Example 3BFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 0

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 9


Check It Out: Example 3CFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 4

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 3


Check It Out: Example 3DFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 1

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 6


Check It Out: Example 3EFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 4

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 7


Check It Out: Example 3FFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 7

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

y = 8


Additional Example 4: Graphing Linear Functions

Graph the function described by the equation. y = 3x+ 2

83(2) + 22

53(1) + 21

23(0) + 20

y3x + 2x

(0, 2)

(1, 5)

(2, 8)


Additional Example 4 Continued

y

2

x 1 2 3 4 5 6 7 8 9

9

87

65

0

1

3

4


Check it out : Example 4A

Graph the function described by the equation. y = x + 3

5(2) + 32

4(1) + 31

3(0) + 30

yx + 3x

(0, 3)

(1, 4)

(2, 5)


Check it out : Example 4A Continued

y

2

x 1 2 3 4 5 6 7 8 9

9

87

65

0

1

3

4


Check it out : Example 4B

Graph the function described by the equation. y = 2x + 5

92(2) + 52

72(1) + 51

52(0) + 50

y2x + 5x

(0, 5)

(1, 7)

(2, 9)

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10


Check it out : Example 4C

Graph the function described by the equation. y = 3x + 3

93(2) + 32

63(1) + 31

33(0) + 30

y3x + 3x

(0, 3)

(1, 6)

(2, 9)

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10


Check it out : Example 4D

Graph the function described by the equation. y = 8 - x

28 - 66

18 - 77

08 - 88

y8 - xx

(8, 0)

(7, 1)

(6, 2)

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

1. Use the given x-values to write solutions as ordered pairs to the equation y = 10x + 5 for x = 0, 1, 2, and 3.

2. Determine whether (4, 2) is a solution to the

equation y = 5x – 6.

No, 2 ≠ 5(4) – 6

(0, 5), (1, 15), (2, 25), (3, 35)


y

2

x 1 2 3 4 5 6 7 8 9

9

87

65

0

1

3

4

3. Graph the function described by the equation y = 5 – x.

Lesson Quiz Cont.


1. Use the given x-values to identify solutions as ordered pairs to the equation y = 7x + 4 for x = 1, 3, 5, and 7.



2. Identify the graph of the function described by the equation y = x – 5.

A. B.


Documents

10-2 Graphing Functions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes