Chap3 Section2

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 3.2 Slope 261 Version: Fall 2007 3.2 Exercises 1. Suppose you are riding a bicycle up a hill as shown below. Figure 1. Riding a bicycle up a hill. a) If the hill is straight as shown, con- sider the slant, or steepness, of its in- cline. As you ride up the hill, what can you say about the slant? Does it change? If so, how? b) The slant is what mathematicians call the slope. To confirm your answer to part (a), you will place the hill on a coordinate system and compute its slope along various segments of the hill. See the figure below. run x (ft) rise y (ft) 0 5 10 15 20 0 5 10 15 20 P (3 , 1) Q (9 , 3) R (12 , 4) Copyrighted material. See: 1 Three points– P , Q and R –have been labeled along the hill. We call the vertical distance (height) the rise and the horizontal distance the run. As you ride up the hill from point P to point Q , what is the rise? What is the run? Use these values to compute the slope from P to Q . c) Now consider as you ride from P to R . What is the rise? What is the run? Use these values to compute the slope from P to R . d) Finally, consider as you ride from Q to R . What is the rise? What is the run? Use these values to compute the slope from Q to R . e) How do the values for slope from parts (b)-(d) compare? Do these results confirm your answer to part (a)? f) Notice that the slope is positive in this example. In this context of rid- ing a bicycle over a hill, what would negative slope mean? 2. Set up a coordinate system on a sheet of graph paper, plotting the points P (3 , 4) and Q ( 2 , 7) and drawing the line through them. a) What can you say about the slope of the line? Is it positive, zero, negative or undefined? Is the slope the same everywhere along the line, or does it change in places? If it does change, where are the slopes different?
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262 Chapter 3 Linear Functions Version: Fall 2007 b) Use your graph to determine the change in y (rise) and the change in x (run). Use these results to compute the slope of the line. c) Use the slope formula to compute the slope of the line. d) Does your numerical solution from part (c) agree with your graphical so- lution from part (b)? If not, check your work for errors. 3. Set up a coordinate system on a sheet of graph paper, plotting the points P ( 1 , 3) and Q (5 , 3) and drawing the line through them. a) What can you say about the slope of the line? Is it positive, zero, negative or undefined? Is the slope the same everywhere along the line, or does it change in places? If it does change, where are the slopes different?
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