graphing relationships

Holt McDougal Algebra 1

Graphing RelationshipsGraphing Relationships

Holt Algebra 1

Warm UpLesson PresentationLesson Quiz


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Graphing Relationships

Warm UpState whether each word or phrase represents an amount that is increasing, decreasing, or constant.

1. stays the same2. rises3. drops4. slows down

constant

decreasing

decreasing

increasing

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Match simple graphs with situations.Graph a relationship.

Objectives

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continuous graphdiscrete graph

Vocabulary

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Graphs can be used to illustrate many different situations. For example, trends shown on a cardiograph can help a doctor see how a patient’s heart is functioning.

To relate a graph to a given situation, use key words in the description.

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Graphing RelationshipsExample 1: Relating Graphs to Situations

Each day several leaves fall from a tree. One day a gust of wind blows off many leaves. Eventually, there are no more leaves on the tree. Choose the graph that best represents the situation.

Step 1 Read the graphs from left to right to show time passing.

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Step 2 List key words in order and decide which graph shows them.

Key Words Segment Description Graphs…

Each day several leaves fallWind blows offmany leaves

Eventually no more leaves

Slanting downwardrapidly

Graphs A, B, and C

Never horizontal Graph B

Slanting downward until reaches zero

Graphs A, B, and C

Example 1 Continued

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Never horizontalSlanting downward rapidlySlanting downward until it reaches zero

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Graphing RelationshipsExample 2

The air temperature increased steadily for several hours and then remained constant. At the end of the day, the temperature increased slightly before dropping sharply. Choose the graph that best represents this situation.

Step 1 Read the graphs from left to right to show time passing .

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Step 2 List key words in order and decide which graph shows them.

Key Words Segment Description Graphs…Increased steadilyRemained constantIncreased slightly before dropping sharply

Slanting upward Graph C

Horizontal Graphs A, B, and C

Slanting upward and then steeply downward Graphs B and C

Step 3 Pick the graph that shows all the key phrases in order. The correct graph is graph C.

Example 2 Continued

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Graphing RelationshipsAs seen in Example 1, some graphs are connected lines or curves called continuous graphs. Some graphs are only distinct points. They are called discrete graphs

The graph on theme park attendance is an example of a discrete graph. It consists of distinct points because each year is distinct and people are counted in whole numbers only. The values between whole numbers are not included, since they have no meaning for the situation.

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Graphing RelationshipsExample 3: Sketching Graphs for Situations

Sketch a graph for the situation. Tell whether the graph is continuous or discrete.A truck driver enters a street, drives at a constant speed, stops at a light, and then continues.

The graph is continuous.

As time passes during the trip (moving left to right along the x-axis) the truck's speed (y-axis) does the following: • initially increases• remains constant• decreases to a stop• increases• remains constant

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When sketching or interpreting a graph, pay close attention to the labels on each axis.

Helpful Hint

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Graphing RelationshipsExample 4: Sketching Graphs for Situations

Sketch a graph for the situation. Tell whether the graph is continuous or discrete.A small bookstore sold between 5 and 8 books each day for 7 days.

The graph is discrete.

The number of books sold (y-axis) varies for each day (x-axis).

Since the bookstore can only sell whole numbers of books, the graph is 7 distinct points.

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Sketch a graph for the situation. Tell whether the graph is continuous or discrete.Jamie is taking an 8-week keyboarding class. At the end of each week, she takes a test to find the number of words she can type per minute. She improves each week.

The graph is discrete.

Each week (x-axis) her typing speed is measured. She gets a separate score (y-axis) for each test.

Since each test score is a whole number, the graph consists of 8 distinct points.

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Sketch a graph for the situation. Tell whether the graph is continuous or discrete.

Example 6

Henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the first valve. He leaves the second valve open until the tank is empty.

As time passes while draining the tank (moving left to right along the x-axis) the water level (y-axis) does the following: • initially declines• decline more rapidly• and then the decline slows down.The graph is continuous.

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Both graphs show a relationship about a child going down a slide. Graph A represents the child’s distance from the ground related to time. Graph B represents the child’s Speed related to time.

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Graphing RelationshipsExample 7: Writing Situations for Graphs

Write a possible situation for the given graph.

A car approaching traffic slows down, drives at a constant speed, and then slows down until coming to a complete stop.

Step 1 Identify labels. x-axis: time y-axis: speed

Step 2 Analyze sections. over time, the speed:• initially decreases,• remains constant,• and then decreases to zero.

Possible Situation:

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Write a possible situation for the given graph

Possible Situation: When the number of students reaches a certain point, the number of pizzas bought increases.

Step 1 Identify labels. x-axis: students y-axis: pizzas

Step 2 Analyze sections. As students increase, the pizzas do the following:• initially remains constant,• and then increases to a new constant.

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Graphing RelationshipsLesson Quiz: Part I

1. Write a possible situation for the given graph.

Possible Situation: The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.

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2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.

Lesson Quiz: Part II

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graphing relationships

Documents

given graph

correct graph

graphing relationshipsexample

graphing relationshipsstep

graphing relationshipsas

graphing relationshipsgraphs

discrete graphsthe graph

downward graphs b