1. “Interpret Graphs”
Preview
Warm Up
California Standards
Lesson Presentation

2. 1. Alessia stopped to tie her shoe.
Warm Up
Alessia walked to the store to buy some groceries. Tell whether her distance from home in each situation 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

3. California
Standards
AF1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

4. 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.

5. 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.

6. Check It Out! 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.

7. 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.

8. 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.

9. 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.

10. 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

11. 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 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.

12. Check It Out! 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.

13. Check It Out! 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

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

15. Lesson Quiz: 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