1. Relating Graphs to Events
3-1
Relating Graphs to Events

2. Geogebra
none

3. Video Tutor Help Interpreting a graph that is related to events
Sketching a graph that is related to events

4. 3-1 Videos Describe rate of change using graphs
In this lesson you will learn to describe the rate of change in a function by analyzing graphs.
Standards: 8.F.B.5
Sketch graphs by interpreting situations
In this lesson you will learn to sketch the graph of a function by interpreting a description.
Standards: 8.F.B.5
Sketch a graph of a linear relation given the function behavior
In this lesson you will learn how to sketch the graph of a linear relation by investigating the equation and verbal description.
Standards: 8.F.B.5
Create a verbal description of a linear relation given a graph or equ...
In this lesson you will learn how to write a verbal description of a linear relation by creating a scenario that fits a graph or equation.
Standards: 8.F.B.5

5. Video Tutor Help Graphing points on the coordinate plane (3-1)
Evaluating algebraic expressions with one variable (3-1)
Write a function with 2 variables

6. Describe function relationships using graphs
In this lesson you will learn to describe function relationships by analyzing a graph.
Standards: 8.F.B.5
Explain intercepts using graphs
In this lesson you will learn to explain the intercepts of a relationship by analyzing graphs.
Standards: 8.F.B.5
Describe rate of change using graphs
In this lesson you will learn to describe the rate of change in a function by analyzing graphs.
Standards: 8.F.B.5
Sketch graphs by interpreting situations
In this lesson you will learn to sketch the graph of a function by interpreting a description.
Standards: 8.F.B.5

7. Describe the rate of change on an interval using a graph
In this lesson you will learn how to describe the behavior of a function on a given interval by examining a graph.
Standards: 8.F.B.5
Describe the rate of change of linear and non-linear functions
In this lesson you will learn how to describe the rate of change of linear and non-linear functions by analyzing a graph.
Standards: 8.F.B.5
Compare two linear relations
In this lesson you will learn how to verbally compare two linear relations by considering the slope and y-intercept of each relation.
Standards: 8.F.B.5
Sketch a graph of a linear relation given the function behavior
In this lesson you will learn how to sketch the graph of a linear relation by investigating the equation and verbal description.
Standards: 8.F.B.5
Create a verbal description of a linear relation given a graph or equ...
In this lesson you will learn how to write a verbal description of a linear relation by creating a scenario that fits a graph or equation.
Standards: 8.F.B.5

8. Worksheets 3-1 Note-Taking Guide 3-1 Practice
3-1 Guided Problem Solving

9. Vocabulary Practice
Chapter 3 Vocabulary (Electronic) Flash Cards

10. Additional Lesson Examples
3-1 Step-by-Step Examples

11. Lesson Readiness
3-1 Problem of the Day
3-1 Lesson Quiz

17. The graph 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.
It gallops at a constant rate
for 20 minutes.
Then it slows down over the next 3 minutes.
It walks at a constant pace for 10 minutes.

18. Additional Example 1: Relating Graphs to Situations
The height of a tree increases over time, but not at a constant rate. Which graph bests shows this? A. B.
As the tree grows, its height increases and then reaches its maximum height. Graph A shows the height of a tree remaining at a constant rate without reaching a maximum height. The answer is graph B.

19. Partner Share! Example 1
The dimensions of the basketball court have changed over the years. However, the height of the basket has not changed. Which graph bests shows this? A. B.
Graph A shows the height of the basket remaining constant. Graph B shows the height increasing without reaching a maximum height. The answer is graph A.

20. Additional Example 2: Sketching Graphs for Situations
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.

21. Additional Example 2 Continued
Step 1: List the different actions you need to show on the graph. The describe the segment for each action.
● Jarod walks inside the store.
● Jarod waits in line.
● Walks to the back of store
Distance from parking lot increases: segment slants upward.
Distance does not change: horizontal segment.
Distance from parking lot increases: segment slants upward.

22. Additional Example 2 Continued
Step 1: List the different actions you need to show on the graph. The describe the segment for each action.
● Walks to the front of the store
● Waits in line.
● Returns to car.
Distance from parking lot decreases: segment slants downward.
Distance does not change: horizontal segment.
Distance from parking lot decreases: segment slants downward.

23. Additional Example 2 Continued
Step 2: Draw the graph.
Time
Distance from car (ft) 20 40 60 80
100
120
walks inside
waits in line
walks to back
walks to front
back to car

24. Partner Share! 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 further 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.

25. Partner Share! Example 2 Continued
Step 1: List the different actions you need to show on the graph. The describe the segment for each action.
● Darcy travels from her house to the Peterman’s house.
● She baby sits for 1 hour.
● After babysitting she travels to the deli
● She eats a sandwich
● She returns home
Distance from home increases: segment slants upward.
Distance does not change: horizontal segment.
Distance from home increases: segment slants upward.
Distance does not change: horizontal segment.
Distance from home decreases: segment slants downward.

26. Partner Share! Example 2 Continued
Step 2: Draw a graph
Time
Distance from house 5 10 20 30 40 50
Drives away from her house
baby sits
drives to deli
eats
drives home

27. Lesson Review: Part I
1. A ball is tossed into the air. Which graph best shows this?
a. b. a
Elevation
Elevation
Time
Time

28. Lesson Review: Part II
2. Sam in-line skated 1000 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.
Distance (m)
500
1,000
1,500
Time

29. Additional Example 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.

30. Additional Example 1 Continued
Step 2 List key words in order and decide which graph shows them.
Key Words
Segment Description
Graphs…
Each day several leaves fall
Wind blows off
many leaves
Eventually no more leaves
Never horizontal
Graph B
Slanting downward
rapidly
Graphs A, B, and C
Slanting downward until reaches zero
Graphs A, B, and C

31. Additional Example 1 Continued
Step 3 Pick the graph that shows all the key phrases in order.
Never horizontal, slanting downward rapidly, slanting downward until reaching zero.
The correct graph is B.

32. Partner Share! Example 1
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 .

33. Partner Share! Example 1 Continued
Step 2 List key words in order and decide which graph shows them.
Key Words
Segment Description
Graphs…
Increased
steadily
Remained constant
Increased slightly before dropping sharply
Slanting upward
Graph C
Graphs A, B, and C
Horizontal
Slanting upward and then steeply downward
Graph C

34. Partner Share! Example 1 Continued
Step 3 Pick the graph that shows all the key phrases in order.
Slanting upward, horizontal, slanting upward and then steeply downward
The correct graph is graph C.

35. As 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.

36. Additional Example 2A: 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 stop sign, and then continues.
As time passes during the trip (moving left to right along the x-axis), the truck's speed
(y-axis) does the following:
Speed
Time y x
• initially increases
• remains constant
• decreases to a stop
• increases
The graph is continuous.

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

38. Additional Example 2B: 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 number of books sold (y-axis) varies for each day (x-axis).
Since the bookstore accounts for the number of books sold at the end of each day, the graph has 7 distinct points.
The graph is discrete.

39. Partner Share! Example 2a
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.
Each week (x-axis) her typing speed is measured. She gets a separate score (y-axis) for each test.
Since each score is separate, the graph consists of distinct units.
The graph is discrete.

40. Partner Share! Example 2b
Sketch a graph for the situation. Tell whether the graph is continuous or discrete.
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:
Water tank
Water Level
Time
• initially declines
• declines more rapidly
• and then the decline slows down.
The graph is continuous.

41. Both graphs below show a relationship about a child going down a slide
Both graphs below 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.

42. Additional Example 3: Writing Situations for Graphs
Write a possible situation for the given graph.
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:
A car approaching traffic slows down, drives at a constant speed, and then slows down until coming to a complete stop.

43. Partner Share! Example 3
Write a possible situation for the given graph
Step 1 Identify labels x-axis: students y-axis: pizzas
Step 2 Analyze sections As students increase, the pizzas bought do the following:
• initially remains constant,
• and then increases to a new constant.
Possible Situation:
When the number of students reaches a certain point, the number of pizzas bought increases.

44. Lesson Review: Part I
1. Write a possible situation for the given graph.
Possible answer: The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.

45. Lesson Review: Part II
2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.

46. Relating Graphs to Events
LESSON 3-1
Additional Examples
Use the graph below.
a. How long did the trip take?
Time is shown on the x-axis. The trip lasted 1 hour, from 7:00 to 8:00.
b. What was the fastest speed?
The fastest speed was 50 mi/h. This speed was maintained between 7:40 and 7:50.

47. Relating Graphs to Events
LESSON 3-1
Additional Examples
An athlete jogs for 30 min, sprints for 5 min, and walks for 10 min. Sketch and label a graph showing his speed.