unit 5: analytic geometry lesson 1: models of movement learning goal i can determine the rate of...

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

Learning Goal

I can determine the rate of change of segments of a time-distance graph.

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

Determine the rate of change (speed) for each segment of the graph.

Mrs. Gonzalez-Day runs each day as part of her daily exercise. The graph shows her distance from home as she runs her route.

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

Can you write a story that describes this graph?

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

During which time segment did Mrs. Gonzalez-Day run the fastest?

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

How long did it take Mrs. Gonzalez-Day to complete her run?

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

Practice

Complete Pg. 197 #1 - 11

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

4 8 12 16 20 24 28 32 36 40 44 48

100

200

300

400

500

600

700Distance vs. Time

Time (min)

A

B

C

D E

F

G

Dis

tan

ce f

rom

Ho

me

(m

)

At 11 o’clock, Billy’s mother sends him to the corner store for milk and tells him to be back in 30 minutes. Examine the graph.

Unit 5: Analytic Geometry

Lesson 1: Models of Movement1.Why are some line segments on the graph

steeper than others? 

 2.Calculate the rate of change (speed) of each of the line segments:

Rate of change AB =

Rate of change BC =

Rate of change CD =

Rate of change DE =

Rate of change EF =

Rate of change FG =

Unit 5: Analytic Geometry

Lesson 1: Models of Movement3.Over what interval(s) of time is Billy travelling the

fastest? the slowest? (Compare steepness, not direction.)

4.How long did it take Billy to reach the store? How do you know?

5.How long did Billy stay at the store?

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

6. How long did it take Billy to get home from the store?

7.How can you use the graph to tell which direction Billy is travelling?

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

8. Did Billy make it home in 30 minutes? How do you know?

9. Using the information the graph provides, write a story that describes Billy’s trip to the store and back.

Unit 5: Analytic Geometry

Lesson 1: Models of Movement

Homework

Pg. 199 #1 - 3