U-DO: For a road with 8% slope; how much of an elevation change occurs for 100 feet of length?

1. S L O P E • U-DO: • For a road with 8% slope; how much of an elevation change occurs for 100 feet of length? • Given the points (3, 4) and (0, 0) and a line passing through them, what is the line’s slope? (7,4) & (1,2)? (-3,2) & (2, -3)? • Graph 2 lines that are parallel to each other by using point pairs (2,2) and (4,3) for one line and (3,3) and (5,4) for the other line. What are their slopes? • ANSWERS: • (change height)/(change length) = slope = 8% = 0.08 = h/100 h = 8 feet • Slope = (y2 – y1)/(x2 – x1) = (4 – 0)/(3 – 0) = 4/3 = 1.33; • (4 – 2)/(7 – 1) = 2/6 = 1/3 = 0.33; • (2 – (-3))/(-3 – 2) = 5/-5 = -1 • 3. Parallel lines have equal slopes. (3 – 2)/(4 – 2) = ½ = (4 – 3)/(5 – 3)

2. S L O P E Perpendicular Lines: Their slopes are negative reciprocals of each other. In other words, slope m1 x slope m2 = -1. If line #1 passes through points (1,1) and (3,2), the slope is (2 – 1)/(3 – 1) = ½. The negative reciprocal of ½ is -2 and is the slope of a line perpendicular to Line #1. From point (3,2) draw this perpendicular line. *Hint: slope = rise/run: (change y)/(change x) • Practice: • 1. State if the lines described by the following point pairs are parallel, perpendicular, or neither: • (0,0) and (4,4) ; (1,-1) and (-2, 2) • (2,1) and (3,5) ; (-1,2) and (2, 14) • (1, 3) and (-2, 3) ; (1,1) and (-3, -6) • Answers: • Perpendicular: 4/4 = 1 and 3/-3 = -1 • Parallel: 4/1 = 12/3 • neither