Making Connections Making Connections with Graphswith Graphs

Focus Activity

Directions:Directions:

Look at each graphLook at each graph Create a situation in which the value Create a situation in which the value

of one variable depends upon the of one variable depends upon the other variableother variable

Your situation must “fit” the graphYour situation must “fit” the graph

TIME

Distance

Joe jogged to the park

He stopped to rest on a bench

Joe walked the rest of the way to the park

What is the dependent variable?

What is the independent variable?

Hours worked

# o

f C

usto

mers

How will our interpretation of the How will our interpretation of the graph change if our axes change?graph change if our axes change?

Interpret This GraphInterpret This Graph

Which pedal is the bus driver using when there is a positive slope? A negative slope?

ActivityActivityTwo-Way InterpretationTwo-Way Interpretation

Divide students into groups of 3Divide students into groups of 3 Distribute Activity Sheets A – DDistribute Activity Sheets A – D Students will interpret each graph Students will interpret each graph

“two ways”“two ways” Students will discuss interpretations Students will discuss interpretations

within groupswithin groups Students will present their Students will present their

interpretations to the class interpretations to the class

InstructionInstruction

Making Making

ConnectionsConnections with Graphswith Graphs

A graph shows a relationship A graph shows a relationship between two variablesbetween two variables

Graphs are used to describe real-life Graphs are used to describe real-life situations.situations.

Graphs demonstrate the relationship Graphs demonstrate the relationship between two variables.between two variables.

This graph represents four people driving This graph represents four people driving cars. Which driver is driving at the fastest cars. Which driver is driving at the fastest rate?rate?

Identify the graph that best represents the relationship between Identify the graph that best represents the relationship between the number of gallons of gasoline Mrs. Jones purchased and the the number of gallons of gasoline Mrs. Jones purchased and the

cost of the gasoline.cost of the gasoline.

TAKS 2003

The graph represents the sales of a CD. Describe The graph represents the sales of a CD. Describe the sales of the CD.the sales of the CD.

When you draw a graph without actual When you draw a graph without actual data, the graph is called a sketch.data, the graph is called a sketch.

Interpret this sketch.Interpret this sketch.

Tom’s commute home

Tom’s Commute Home:Tom’s Commute Home:

Name your independent variableName your independent variable

Name you dependent variableName you dependent variable

The line touches the x axis three times. What does this represent?

Remember!Remember!

Rate of changeRate of change is a term which is a term which describes the SLOPEdescribes the SLOPE

Rate of change = Rate of change = riserise runrun

Rate of change = Rate of change = ΔΔ yy or or change in change in yy ΔΔ xx change in change in xx

WHY?WHY?

Why do you think “slope” is referred Why do you think “slope” is referred to as “rate of change”?to as “rate of change”?

Find the rate of changeFind the rate of change

Find the rate of change

Interpreting Graphs: StepsInterpreting Graphs: Steps Study the graph Study the graph Identify the quantities that are being Identify the quantities that are being

comparedcompared Look for trends – Understand what Look for trends – Understand what

relationship the graph is describingrelationship the graph is describing Look at the scales used on the axes of the Look at the scales used on the axes of the

graphgraph Look for a pattern in the data – increases, Look for a pattern in the data – increases,

decreases, or data that remain constantdecreases, or data that remain constant Translate your observations into statementsTranslate your observations into statements Example: As distance increases, speed Example: As distance increases, speed

decreasesdecreases

Any Questions?Any Questions?