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Class Objective for August 31

Continuing from Friday’s lesson, we will again focus on the meaning of “rate of

change” in various situations. Thinking again about what rate of change represents? How

it can be used? As we graph our results, think about how participants’ rates of

change compare to each other, algebraically and graphically.

2-54 The Big Race – Heat 2

In the second heat, Elizabeth, Kaye, and Hannah raced down the track.  They knew the winner would compete against the other heat winners in the final race. 

When the line representing Kaye’s race is graphed, the equation is f(x) = 2/3x + 1.  What was her speed (in meters per second)?  Did she get a head start? 

Elizabeth’s race is given by the equation f(x) = 12/16x + 4.  Who is riding faster, Elizabeth or Kaye?  How do you know? 

Just as she started pedaling, Hannah’s shoelace came untied!  Being careful not to get her shoelace tangled in the pedal, she rode slowly.  Hannah’s race is represented by the table to the right.  At what unit rate was she riding?  Write your answer as a unit rate. 

To entertain the crowd, a clown rode a tricycle in the race described by the equation  f(x) = 20 − x.  Without graphing or making a table, fully describe the clown’s ride. 

2-56: Take A Walk

2-56. TAKE A WALK The president of the Line Factory is so impressed with your work that you have been given a special assignment: to analyze the graph below, which was created when a customer walked in front of a motion detector.  The motion detector recorded the distance between it and the customer. 

The graph is a piecewise graph.  A piecewise graph is a graph that has a different equation for different intervals along the x-axis.  Working with your team, explain the motion that the graph describes.

Make sure you describe: If the customer was walking toward or away from the motion detector.

Where the customer began walking when the motion detector started collecting data.

Any time the customer changed direction or stopped. When the customer walked slowly and when he or she walked

quickly by calculating the rate of change.  Find the speed in feet per second.

The domain (the interval along the x‑axis) for which each of the equations is valid.

Preview and Review

2-64. Use what you know about y = mx + b to graph each of the following equations quickly on the same set of axes.

y = 3x + 5 y = −2x + 10 y = 1.5x

Preview and Review

2-65. Find the equation of the line graphed at right.

What are its x- and y-intercepts?

Classwork for Today

2-61, 2-55, 2-57

Homework for Tomorrow

2-59, 2-60, 2-62, 2-63, 2-67