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Learn to relate graphs to situations . You can use a graph to show the relationship between speed and time, time and distance, or speed and distance. Emma exercises her horse. We will graph this story. The horse walks at a constant speed for the first 10 minutes. 20. Speed (mi/hr).
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You can use a graph to show the relationship between speed and time, time and distance, or speed and distance.
Emma exercises her horse. We will graph this story. The horse walks at a constant speed for the first 10 minutes. 20 Speed (mi/hr) 2. Its speed increases over the next 7 minutes 10 3. Then it gallops at a constantrate for 20 minutes. 10 20 0 30 40 50 Time (min) 4. It slows down over the next 3 minutes. 5. Then walks at a constant pace for 10 minutes. How long did Emily exercise her horse?
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? B. A. C. How does a tree usually grow? Graph A shows the height of a tree not increasing but remaining constant. Graph B shows the height of a tree increasing, not at a constant rate and reaching a maximum height. Graph C shows the height of a tree increasing at a constant rate without reaching a maximum height.
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? C. A. B. 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.
Additional 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.
1 Understand the Problem Additional Example 2 Continued 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.
Make a Plan 120 100 Distance from car (ft) 80 60 40 20 2 0 Time Additional Example 2 Continued Sketch a graph that represents the situation. Then use the graph to find the total distance Jarod traveled.
3 Solve 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. Jarod traveled a total of 200 feet.
4 Additional Example 2 Continued Look Back 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.
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.
1 Understand the Problem Check It Out: Example 2 Continued 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.
Make a Plan 50 40 30 Distance from house 20 10 5 2 Time 0 Check It Out: Example 2 Continued Sketch a graph that represents the situation. Then use the graph to find the total distance Darcy traveled.
3 Solve 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. Darcy traveled a total of 60 miles.
4 Check It Out: Example 2 Continued Look Back 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.
Lesson Quiz: Part I 1. A ball is tossed into the air. Which graph best shows this? a. b. b Elevation Elevation Time Time
1,500 Distance (m) 1,000 500 Time Lesson Quiz: Part II 2. 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. 2,000 m
Take out agenda • Write down the following: • Homework, Due Wednesday • Workbook, Page 38
