Use this information for Exercises 33 and 34. Like many U.S. cities Evanston, Illinois, has building codes to regulate the steepness of driveways and parking garage ramps. A residential driveway can have a maximum slope of 12%, and the maximum slope of a ramp in an indoor parking garage is 15%. (www.cityofevanston.org) 33) A homeowner calls a landscape architect to tear out his old driveway and design a new one. The new driveway will have a different slope and will be constructed of brick pavers. In the new plans, the difference in height between the top and the bottom of the driveway will be 4 ft, and the linear distance between those two points will be 40 ft. Does the driveway meet the building code? Explain your answer. 34) The fi rm hired to build a parking garage in downtown Evanston wants to use plans from a garage it built in another city. In that structure, the ramps rose 1 ft for every 6.25 ft of horizontal distance. Can the construction fi rm use the same ramp plans in Evanston, or will it have to redesign them? Explain your answer. 35) Melissa purchased a new car in 2008. The graph shows the value of the car from 2008–2012. x y Value of the Car 2012 2008 2010 Year Value $22,000 $18,000 $14,000 $10,000 $6000 $2000 a) What was the value of the car in 2008? b) Without computing the slope, determine whether it is positive or negative. c) What does the sign of the slope mean in the context of this problem? d) Find the slope of the line segment, and explain what it means in the context of the problem. 15) Graph a line with a positive slope and a negative x-intercept. 16) Graph a line with a negative slope and a positive y-intercept. Use the slope formula to fi nd the slope of the line containing each pair of points. 17) (3, 2) and (9, 5) 18) (4, 1) and (0, 5) 19) (2, 8) and (2, 4) 20) (3, 2) and (1, 6) 21) (9, 2) and (0, 4) 22) (5, 1) and (2, 4) 23) (3, 5) and (1, 5) 24) (4, 4) and (4, 10) 25) (3, 2) and (3, 1) 26) (0, 7) and (2, 7) 27) a3 8 , 1 3 b and a1 2 , 1 4 b 28) a3 2 , 7 3 b and a1 3 , 4b 29) (4.8, 1.6) and (6, 1.4) 30) (1.7, 1.2) and (2.8, 10.2) Objective 3: Use Slope to Solve Applied Problems 31) The slope of a roof is sometimes referred to as a pitch. A garage roof might have a 10-12 pitch. The fi rst number refers to the rise of the roof, and the second number refers to how far over you must go to attain that rise (the run). Rise Run a) Find the slope of a roof with a 10-12 pitch. b) Find the slope of a roof with an 8-12 pitch. c) If a roof rises 8 in. in a 2-ft run, what is the slope of the roof? How do you write the slope in x-12 pitch form? 32) To make all buildings wheelchair accessible, the federal government has mandatory specifi cations for the slope of wheelchair ramps in new construction. A wheelchair ramp can have a maximum slope of 1 12 . Does the following ramp meet this requirement? (www.access-board.gov) 26 ft 2 ft www.mhhe.com/messersmith SECTION 4.2 Slope of a Line and Slope-Intercept Form 167
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