MSA Investigation 1 – Additional Practice 1) Learning Target: Added practice with linear relationships 2) MSA Inv 1 Day 5 Homework: Complete all pages in the packet. Get a signature on the packet. 3) CHECK UP QUIZ #1 on Tuesday, Jan 31 4) Warm Up: (packet pg. 13) Jose, Mario, Melanie, Mike, and Alicia are on a weeklong cycling trip….

1. Assume that each person cycles Jose, Mario, Melanie, Mike, and Alicia are on a weeklong cycling trip. The table below gives the distance Jose, Mario, and Melanie travel for the first 3 hours. Cycling times include only biking time, not time to eat, rest, and so on. 1. Assume that each person cycles at a constant rate. Find the rate at which each person travels during the first 3 hours. Jose: Mario: Melanie: 5 mph 7 mph 9 mph

KEY: Jose Mario Melanie 3. Graph the time and distance data for all three riders on the same coordinate axes. Use different colors for each person. Cycling with Friends KEY: Jose Mario Melanie 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 110 Distance (Miles) 4. Use the graphs to find the distance each person travels in 6 ½ hours. Hours cycled

y = mx + b Jose: Mario: Melanie: 2. Find the distance each person travels in 7 hours. y = mx + b Jose: Mario: Melanie: 35 miles = 5 mph (7hrs) 49 miles = 7 mph (7hrs) 63 miles = 9 mph (7hrs)

KEY: Jose Mario Melanie 5. Use the graphs to find the time it takes each person to travel 70 miles. Cycling with Friends KEY: Jose Mario Melanie 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 110 Distance (Miles) 6. How does the rate at which each person rides affect the graph? Hours cycled

Jose: Mario: Melanie: d = 5t 32.5 = 5(6.5) d = 7t 45.5 = 7(6.5) d = 9t 7. For each rider, write an equation to calculate the distance traveled after a given number of hours. y = mx + b Jose: Mario: Melanie: d = 5t 32.5 = 5(6.5) d = 7t 45.5 = 7(6.5) d = 9t 58.5 = 9(6.5) 8. Use your equations from the previous question to calculate the distance each person travels in 6 ½ hours.

Jose: 5 Mario: 7 Melanie: 9 y = mx + b 9. How does a person’s cycling rate show up in his or her equation? y = mx + b It is the slope or the coefficient. It is placed before, and multiplied by, the independent variable. 10. Are any of these proportional relationships? If so, what is the constant of proportionality? Yes, they are all proportional Jose: 5 Mario: 7 Melanie: 9

11. Mike makes the following table of the distances he travels during the first day of the trip. a. Suppose Mike continues riding at this rate. Write an equation for the distance d Mike travels after t hours. y = mx + b d = mt d = 6.5t

distance time (hours) b. Sketch a graph of the equation. i. How did you choose the range of values for the time axis? Mike’s cycling trip 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 distance ii. How did you choose the range of values for the distance axis? time (hours)

c. How can you find the distances Mike travels in 7 hours and 9 ½ hours using the table? 45.5 8 52 9 58.5 10 65

distance time (hours) Mike’s cycling trip d. How can you find the distances Mike travels in 7 hours and 9 ½ hours using the graph? 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 distance time (hours)

TABLE EQUATION d = 6.5t 100 = 6.5(15.38) 237 = 6.5(36.5) GRAPH g. How can you find the number of hours it takes Mike to travel 100 miles and 237 miles using the ________? TABLE EQUATION d = 6.5t 100 = 6.5(15.38) 237 = 6.5(36.5) GRAPH 10 15 20 25 30 35 40 45 5 50 300 275 250 225 200 175 150 125 100 75 time (hours) distance Mike’s cycling trip 10 65 15.38 100 130 200 36.5 237

i. What are the advantages and disadvantages of using each model in parts c-h?   Advantages Disadvantages Table Graph Equa-tion

Melanie: 9 miles per hour j. Compare the rate at which Mike rides with the rates at which Jose, Mario, and Melanie ride. Who rides the fastest? Mike: 6.5 miles per hour Jose: 5 miles per hour Mario: 7 miles per hour Melanie: 9 miles per hour

i. How can you determine this from the tables?

KEY: Jose Mario Melanie Mike ii. How can you determine this from the graphs? KEY: Jose Mario Melanie Mike Cycling with Friends 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 110 Distance (Miles) Hours cycled

Mike: d = 6.5t Jose: d = 5t Mario: d = 7t Melanie: d = 9t iii. How can you determine this from the equations? Mike: d = 6.5t Jose: d = 5t Mario: d = 7t Melanie: d = 9t

will determine the total hours she will travel. 12. The distance in miles Alicia travels in t hours is represented by the equation d = 7.5t. a. At what rate does Alicia travel? Explain. 7.5 miles per hour The number of hours she travels times her travel rate of 7.5 miles per hour will determine the total hours she will travel.

b. Suppose the graph of Alicia’s distance and time is put on the same set of axes as Mike’s, Jose’s, Mario’s, and Melanie’s graphs. Where would it be located in relationship to each of the graphs? Describe the location without actually making a graph. Cycling with Friends 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 110 Alicia would be faster than Jose and Mike, and just barely faster than Mario. But Alicia would be slower than Melanie. Distance (Miles) Hours cycled

MSA Investigation 1 – Additional Practice Did I reach my Learning Target? Additional practice with linear relationship concepts. Homework: Complete all pages in the packet. Get a signature on the packet. CHECK UP QUIZ #1 on Tuesday, Jan 31 (No school on Monday)