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Algebra B Name ___________________________

Unit 7 – Linear Relationships Date ______________Period_________

What can slope represent?

Slope as a measurement of Rate

Today you will focus on the meaning of slope in various contexts. What does a slope represent? How can you use it?

1. THE BIT RACE – HEAT 1

Before a big race, participants often compete in heats, which are preliminary races that determine who competes in the final race. Later, your class will compete in a tricycle race against the winners of these preliminary heats.

In the first heat, La’mifa, Bretlynn, and Honey-Girl rode tricycles toward the finish line. La’mifa began at the starting line and rode at a constant rate of 2 meters every second. Bretlynn got an 8-meter head start and rode 2 meters every 5 seconds. Honey-Girl rode 5 meters every 4 seconds and got a 6-meter head start.

a. On neatly scaled axes, graph and write an equation in terms of x and y for the distance La’mifa travels. Let x represent time in seconds and y represent distance in meters. Then do the same for Bretlynn and Honey-Girl using the same set of axes.

b. After how many seconds did La’mifa catch up to Honey-Girl? How far were they from the starting line when La’mifa caught up to Honey-Girl? Confirm your answer algebraically.

c. If the race is 20 meters long, who won? Use both the graph and the rules to justify your answer.

d. What is the slope of Bretlynn’s line? How does the slope of her line explain her rate of travel (also known as her speed)?

e. Yashimi also rode in this heat. When her distance line is graphed, the rule is y = [pic]x + 1. What was her speed? Did she get a head start?

2. OTHER RATES OF CHANGE

Problem 1 concentrated on situations where the slope of a line represented speed. However, any other situations can be graphed that do not involve motion. Examine the graphs below and explain what real-world quantities the slope and y- intercepts represent. Find the slope and y-intercept. Write the measurement units with each of your answers. (For example, the slopes in problem 1 would be expressed in meters per second.)

[pic]

Review/Preview

1. THE BIG RACE – HEAT 2

Barla, Elizamita, and J-Money participated in the second heat of “The Big Race.” Barla thought she could win with a 3-meter head start even though she only pedaled 3 meters ever 2 seconds. Elizamita began at the starting line and finished the 20-meter race in 5 seconds. Meanwhile, J-Money rode his tricycle so that his distance (y) from the starting line in meters could be represented by the rule y = [pic]x + 1, where x represent time in seconds.

a. Using the given information, graph lines for Barla, Elizamita, and J-Money on the same set of axes. Who won the 20-memter race and will advance to the final race?

b. Find rules that describe Barla’s and Elizamita’s motion.

c. How fast did J-Money pedal?

d. When did J-Money pass Barla? Confirm your answer algebraically.

2. Salami and More Deli sells a 6-food sandwich for parties. It weighs 8 pounds. Assume the weight per foot is constant.

a. How much does a sandwich 0 feet long weigh?

b. Draw a graph showing the weight of the sandwich (vertical axis) compared to the length of the sandwich (horizontal axis). Label the axes with appropriate units.

c. Use your graph to estimate the weight of a 1-foot sandwich.

d. Write a proportion to find the length of a 12-pound sandwich.

3. Create a table and a graph for the line y = 5x -10. Find the x-intercept and y- intercept in the table and in the graph.

4. Match each expression in the left column with the equivalent expression on the right. Show and explain how you decided which ones matched.

5. Complete the missing entries in the table below. Then write the rule.

IN (x) |2 |10 |6 |7 |3 | |10 |100 |x | |OUT (y) |4 |28 |16 | | |10 | | | | |

Rule:

6. Write and solve an equation (or a system of equations) for the situation below. Define your variable(s) and write your solution as a sentence.

The Physical Education Department sells t-shirts for $12 and shorts for $8. One month, they sold 77 total items for $780 in total. How many t-shirts did they sell?

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