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2.2 Find Slope and Rate of Change Example 1 The roof of an entryway to an office building has a rise of 40 feet and a run of 100 feet. What is its slope?
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2.2 Find Slope and Rate of Change Example 2 What is the slope of the line passing through the points (-4, -5), (6, -2)? If (x1, y1) = (2, 1) and (x2, y2) = (-1, 3), would the slope be different?
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2.2 Find Slope and Rate of Change Example 3 Without graphing , tell whether the line through the given points rises, falls, is horizontal or is vertical. (1, 6), (8, -1) (-4, -3), (7, 1) (-5, 3), (-5, 1) (9, 2), (-9, 2)
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2.2 Find Slope and Rate of Change Two lines that do not intersect are called parallel lines. Two lines that intersect to form a right angle are called perpendicular lines. Using slopes we can determine whether two different non vertical lines are parallel or perpendicular.
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2.2 Find Slope and Rate of Change Example 4 Tell whether the lines are parallel, perpendicular or neither. Line 1: (-2, 1) and (0, -5); Line 2: (0, 1) and (-3, 10) Line 1: (-5, 3) and (-2, -3); Line 2: (4, 11) and (-4, -5)
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2.2 Find Slope and Rate of Change If two lines are parallel what do we know about their y-intercepts? If one of two perpendicular lines has a slope of 1/a and a<0, is the slope of the other line positive or negative?
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2.2 Find Slope and Rate of Change Another term for slope is rate of change, where a rate is a ratio of two quantities that have different units. Real life rate of change has units like miles per hour or degrees per pay.
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2.2 Find Slope and Rate of Change Example 5 Predict the percent of forestland in New Hampshire in 2005. 1983 – 87% forested 2001 – 81.1% forested.
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2.2 Find Slope and Rate of Change How do you determine whether two nonvertical lines are parallel or perpendicular?
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