5-5 graphing linear functions warm up warm up lesson presentation lesson presentation problem of the...

5-5 Graphing Linear Functions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpInterpret the graph.

A rocket is fired into the air.

The rocket’s speed increases until gravity gradually slows the rocket and causes it to fall to the ground.

Rocket

Sp

eed

Time

y

x


Problem of the Day

The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers?25 and 92


Learn to identify and graph linear equations.


Vocabulary

linear equation

linear function


The graph at right shows how far a kayak travels down a river if the current flows 2 miles per hour. The graph is linear because all the points fall on a line. It is part of the graph of a linear equation.

A linear equation is an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph. Linear equations and linear graphs can be different representations of linear functions. A linear function is a function whose graph is a nonvertical line.

y

02 4

2

4

6

x

Miles

Hours0


Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair.


Graph the linear function y = 4x - 1.

Additional Example 1: Graphing Linear Functions

Input Rule Output Ordered Pair

x 4x – 1 y (x, y)

0

1

–1

4(0) – 1

4(1) – 1

4(–1) – 1

–1

3

–5

(0, –1)

(1, 3)

(–1, –5)


Additional Example 1 Continued

Graph the linear function y = 4x - 1.

Place each ordered pair on the coordinate grid and then connect the points with a line.

x

y

0–2–4 2 4

2

4

–2

–4

(0, –1)

(1, 3)

(–1, –5)


Graph the linear function y = 3x + 1.

Input Rule Output Ordered Pair

x 3x + 1 y (x, y)

0

1

–1

3(0) + 1

3(1) + 1

3(–1) + 1

1

4

–2

(0, 1)

(1, 4)

(–1, –2)

Check It Out: Example 1


Check It Out: Example 1 Continued

Graph the linear function y = 3x + 1.

Place each ordered pair on the coordinate grid and then connect the points with a line.

x

y

0–2–4 2 4

2

4

–2

–4

(0, 1)

(1, 4)

(–1, –2)


The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Scientists began studying two parts of these plates when they were 30 centimeters apart. Write a linear function that describes the movement of the plates over time. Then make a graph to show the movement over 4 years.

Additional Example 2: Earth Science Application

Begin by making a function table. Include a column for the rule.



OutputRuleInput

15(x) + 30x

0

2

4

15(0) + 30

15(2) + 30

15(4) + 30

y

30

60

90

Let x represent the input and y represent the output.

Multiply the input by 15 and then add 30.

The function is y = 15x + 30, where x is the number of years and y is the total centimeters apart the two plates are.



Graph the ordered pairs (0, 30), (2, 60), and (4, 90) from your table. Connect the points with a line.

x

y100

80

60

40

20

0 2 4 8 10 12

Cen

tim

ete

rs

Years

Check

Substitute the orderedpairs into th functiony = 15x + 30.

30 = 15(0) + 30 ?

30 = 30?

90 = 15(4) + 30 ?

90 = 90?


Check It Out: Example 2

Dogs are considered to age 7 years for each human year. If a dog is 3 years old today, how old in human years will it be in 4 more years? Write a linear equation which would show this relationship. Then make a graph to show how the dog will age in human years over the next 4 years.

Begin by making a function table. Include a column for the rule.


Check It Out: Example 2 Continued

OutputRuleInput

7(x) + 21x

0

2

4

7(0) + 21

7(2) + 21

7(4) + 21

y

21

35

49

Let x represent the input and y represent the output.

Multiply the input by 7 and then add 21.

The function is y = 7x + 21, where x is the number of years and y is the total age of the dog in human years.


Check it Out: Example 2 Continued

x

Check

Substitute the orderedpairs into th functiony = 15x + 30.

30 = 15(0) + 30 ?

30 = 30?

90 = 15(4) + 30 ?

90 = 90?

Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line.

y

80

60

40

20

0 2 4 8 10

Hu

man

Year

Years


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Graph the linear functions.

1. y = 3x – 4

2. y = –x + 4

3. y = 2

y = 3x – 4

y = –x +4

y = 2


Lesson Quiz: Part II

4. The temperature of a liquid is decreasing at a rate of 12°F per hour. Susan begins measuring the liquid at 200°F. Write a linear function that describes the change in temperature over time. Then make a graph to show the temperature over 5 hours.

y = 200 – 12x


1. Identify the graph of the linear function y = 2x – 5.

A. B.



2. Identify the graph of the linear function y = –x + 4.

A. B.



3. Identify the graph of the linear function y = 5.

A. B.



4. Larry has 150 cents in his piggy bank. He puts 20 cents into it everyday. Identify a linear function that describes the amount in the piggy bank over time and a graph that shows the amount over 5 days.

A. y = 150 – 20x B. y = 150 + 20x


5-5 graphing linear functions warm up warm up lesson presentation lesson presentation problem of the...

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