Interpreting Graphs 5-2

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

Speed (mi/hr) ‏ 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 constant rate 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

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.

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. C.

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.

Additional Example 2 Continued 1 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.

Additional Example 2 Continued Sketch a graph that represents the situation. Then use the graph to find the total distance Jarod traveled. 2 Make a Plan Time Distance from car (ft) ‏

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. Solve 3 Jarod traveled a total of 200 feet.

Additional Example 2 Continued Look Back 4 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.