Course 2

4-3 Interpreting Graphs4-3 Interpreting Graphs

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

4-3 Interpreting Graphs

Warm UpAlessia walked to the store to buy some groceries. Tell whether her position in each story is best represented by a line with positive, negative, or zero slope.

1. Alessia stopped to tie her shoe.

2. Alessia walked from home to the

store.

3. Alessia ran home from the store.

zero

positive

negative

Course 2

4-3 Interpreting Graphs

Problem of the Day

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

x 4 2 0 2 4

y 4 2 0 2 4

Course 2

4-3 Interpreting Graphs

Learn to relate graphs to situations .

Course 2

4-3 Interpreting Graphs

You can use a graph to show the relationship between speed and time, time and distance, or speed and distance.

Course 2

4-3 Interpreting Graphs

Speed (mi/hr)

10

20

10 20 30 40 50

The graph at the right shows the varying speeds at which Emma exercises her horse. The horse walks at a constant speed for the first 10 minutes. Its speed increases over the next 7 minutes, and then it gallops at a constantrate for 20 minutes. Then it slows down over the next 3 minutes and then walks at a constant pace for 10 minutes.

Time (min)0

Course 2

4-3 Interpreting Graphs

The height of a tree increases over time, but not at a constant rate. Which graph bests shows this?

Additional Example 1: Relating Graphs to Situations

As the tree grows, its height increases and then reaches its maximum height. Graph A shows the height of a tree not increasing but remaining constant. Graph C shows the height of a tree increasing at a constant rate without reaching a maximum height. The answer is graph B.

A. B. C.

Course 2

4-3 Interpreting Graphs

Check It Out: Example 1The dimensions of the basketball court have changed over the years. However, the height of the basket has not changed. Which graph bests shows this?

Graph A shows the height of the basket remaining constant. Graph C shows the height increasing without reaching a maximum height. Graph B shows the height increasing then remaining constant over time. The answer is graph A.

A. B. C.

Course 2

4-3 Interpreting GraphsAdditional Example 2: Problem Solving

Application

Jarod parked his car in the supermarket parking lot and walked 40 ft into the store and to the customer service counter, where he waited in line to pay his electric bill. Jarod then walked 60 ft to the back of the store to get 2 gallons of milk and walked 50 ft to the checkout near the front of the store to pay for them. After waiting his turn and paying for the milk, he walked back 50 ft to his car. Sketch a graph to show Jarod’s distance from his car over time. Use your graph to find the total distance traveled.

Course 2

4-3 Interpreting Graphs

Additional Example 2 Continued

11 Understand the Problem

The answer will be the total distance that Jarod traveled.

List the important information:● Jarod walked from the parking lot directly to t the customer service counter and waited in t line.● Jarod then walked to the back of the store for t milk and then to the checkout at the front t and waited in line. ● Then Jarod returns to his car.

Course 2

4-3 Interpreting Graphs

Additional Example 2 Continued

Sketch a graph that represents the situation. Then use the graph to find the total distance Jarod traveled.

22 Make a Plan

Time

Distance from car

(ft)

0

20

40

60

80

100

120

Course 2

4-3 Interpreting Graphs

Additional Example 2 Continued

The distance increases from 0 to 40 feet when Jarod walks from the parking lot, where he parked his car, to the supermarket customer service counter. The distance does not change while he waits in line to pay his bill. The distance increases by 60 feet when he walks to the back of the store to get milk. The distance decreases as he walks back 50 feet to the checkout near the front of the supermarket. The distance does not change as he waits in line to pay for the milk. The distance decreases again as he walks another 50 feet back to his car in the supermarket parking lot.

Solve33

Jarod traveled a total of 200 feet.

Course 2

4-3 Interpreting Graphs

Additional Example 2 Continued

Look Back44

Jarod walked from the supermarket parking lot to the back of the supermarket, approximately 100 feet. From the back of the supermarket he then returned to the parking lot, an additional 100 feet. The answer, 200 feet is reasonable since 100 plus 100 equals 200.

Course 2

4-3 Interpreting Graphs

Check It Out: Example 2

Darcy traveled 22 miles from her house to the Peterman’s house were she babysat for 1 hour. After babysitting she traveled 8 miles to the deli to buy a sandwich. After eating her sandwich she returned home. Sketch a graph to show Darcy’s distance from her house over time. Use your graph to find the total distance traveled.

Course 2

4-3 Interpreting Graphs

Check It Out: Example 2 Continued

11 Understand the Problem

The answer will be the total distance that Darcy traveled.

List the important information:

• Darcy traveled from her house 22 miles directly to the Peterman’s house and babysat for 1 hour.

• Darcy then traveled 8 miles to the deli where she ate a sandwich.

• Darcy then traveled home.

Course 2

4-3 Interpreting Graphs

Check It Out: Example 2 Continued

Sketch a graph that represents the situation. Then use the graph to find the total distance Darcy traveled.

22 Make a Plan

Time

Distance from

house

0

5

10

20

30

40

50

Course 2

4-3 Interpreting Graphs

Check It Out: Example 2 Continued

The distance increases from 0 to 22 miles when Darcy travels from her house to the Peterman’s house. The distance does not change while she baby-sits. The distance increases by 8 miles when she travels to the deli. The distance does not change as she eats her sandwich. The distance decreases as she travels home.

Solve33

Darcy traveled a total of 60 miles.

Course 2

4-3 Interpreting Graphs

Check It Out: Example 2 Continued

Look Back44

The Peterman’s house is 22 miles from her house, so Darcy had to travel that distance twice just to go to their house and return. The answer, 60 miles, is reasonable since it is greater than 44 miles.

Course 2

4-3 Interpreting Graphs

Lesson Quiz: Part I1. A ball is tossed into the air. Which

graph best shows this?

a. b.

b

Elevation

TimeElevation

Time

Course 2

4-3 Interpreting Graphs

Lesson Quiz: Part II2. Sam in-line skated 1,000 m from his

home to the park, where he rested on a bench. He then returned home. Sketch a graph to show the distance he in-line skated compared to time. Use your graph to find the total distance traveled.

Distance (m)

500

1,000

1,500

Time

2,000 m