5-3 graphing proportional relationships warm up warm up lesson presentation lesson presentation...

5-3 Graphing Proportional Relationships

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm Up Identify the quadrant that contains each point.1.(6, –4)

2. (5, 3)

3. (–5, –2)

IV

I

III


Problem of the Day

Graph the ordered pairs form the table. What letter do the points form? V


MA.7.A.1.4 Graph proportional relationships…

Sunshine State Standards


Vocabulary

linear equation

linear function


The table shows how far a kayak travels down a river if the kayak is moving at a rate of 2 miles per hour.

y

02 4

2

4

6

x

Miles

Hours0

Notice for all ordered pairs in the table for every 1 hour increase in time, the miles traveled increases by 2. These ordered pairs are in proportion.

1 2

= = =2 4

3 6

3 8

If the ordered pairs are in proportion, then the data represents a proportional relationship. When you graph a proportional relationship, the result is a line that passes through the origin.


Graph the linear function y = 4x.

Additional Example 1: Graphing Proportional Relationships

x 0 1 2 3

y 0 4 8 12

Proportional relationships pass through (0, 0).

Graph the ordered pairs (0, 0), (1, 4), (2, 8), (3, 12).

Make a table.


Additional Example 1 Continued

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

y

4

8

6

2

(1, 4)

(2, 8)

(0, 0) x

The graph is a straight line that passes through the origin.

Check

1 4

= =2 8

3 12

The ordered pairs are proportional.

10

(3, 12)

2 4 6 8 10

12

0


Graph y = 15x.

Check It Out: Example 1

x 0 1 2 3

y 0 15 30 45

y

40

20

x

60

2 4 6 8 0


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.


Some relationships are linear but not proportional. If the ordered pairs in a linear function are not all proportional then it is not a proportional relationship. These non-proportional relationships do not pass through the origin on a graph.


Tell whether the function is a proportional relationship. Then graph the function.

Additional Example 2: Identify Proportional Relationships

The ordered pairs are proportional and the graph passes through (0, 0). y = –2x is a proportional relationship.

x –1 0 1 2 3y 2 0 –2 –4 –6

–1 2

1 –2

= = = 2 –4

3 –6

Make a table.A. y = –2x


Tell whether y = 10x – 1 is a proportional relationship. Then graph the function.


x 0 1 2 3 4y

The ordered pairs are not proportional, and the graph does not pass through (0, 0). y = 10x –1 is not a proportional relationship.

–1 9 19 29 39


The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Write a linear function that describes the movement of the plates over time. Graph the relationship. Is this a proportional relationship? Justify your answer.

Additional Example 3: Earth Science Application

Let x represent the input, which is the time in years. Let y represent the output, which is the distance in centimeters the plates move apart.

distance in cm 15 cm/yr time in years=

y 15 x=

The function is y = 15x. Yes, the graph goes through the origin


Additional Example 3 Continued

OutputRuleInput

15(x)x

0

1

2

15(0)

15(1)

15(2)

y

0

15

30

Multiply the input by 15.

Make a function table. Include a column for the rule.

3 15(3) 45


Additional Example 3 ContinuedGraph the ordered pairs (0, 0), (1, 15), (2, 30), and (3, 45) 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

CheckUse the ordered pairs (1, 15), (2, 30), and (3, 45) to see if the relationship is proportional.

1 15

2 30

= = 3 45

The ordered pairs are proportional and the graph passes through (0, 0). y = 15x is a proportional relationship.



The outside temperature is increasing at the rate of 6 °F per hour. When Reid begins measuring the temperature, it is 52 °F. Write a linear function that describes the outside temperature over time. Graph the relationship. Is this a proportional relationship? Justify your answer.

y = 6x + 52, where x is thenumber of hours and y is the temperature.The ordered pairs are not proportional andthe graph does not pass through (0, 0).y = 6x + 52 is not a proportional relationship.


Check it Out: Example 3 Continued

100

80

60

40

0 2 4 6 8

Tem

pera

ture

Hours


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Tell whether each function is a proportional relationship. Then graph the function.

1. y = 3x – 4

2. y = –x

3. y = 2x

y = 3x – 4

y = –x

y = 2x

no

yes

yes


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; no, the graph does not go through the origin.


1. Tell whether the linear function y = 2x is a proportional relationship.

A. yes

B. no



2. Tell whether the graph of the given linear function is a proportional relationship.

A. yes

B. no



3. 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. Is this a proportional relationship?

A. y = 20x; yes

B. y = –20x; yes

C. y = 150 + 20x; no

D. y = 150 – 20x; no


5-3 graphing proportional relationships warm up warm up lesson presentation lesson presentation...

Documents

proportional relationships

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linear function y

ordered pairs

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x01234 y

v slide

linear graphs