2.2 S LOPE AND R ATE OF C HANGE Algebra 2. F INDING S LOPES OF L INES.

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Presentation transcript:

2.2 S LOPE AND R ATE OF C HANGE Algebra 2

F INDING S LOPES OF L INES

E XAMPLES Find the slope of the line passing through (-2, -4) and (3, -1) Find the slope of the line passing through (1, -5) and (-2, 3)

C LASSIFICATION OF L INES BY S LOPE A line with a positive slope rises from left to right A line with a negative slope falls from left to right A line with a slope of zero is horizontal A line with an undefined slope is vertical

E XAMPLES Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical a) (-2, 3), (1, 5) b) (1, -2), (3, -2) c) (1, -4), (6, -5)

S TEEPNESS OF L INES Positive Slopes with the greater slope number is steeper Negative Slopes with the greater slope number is steeper

E XAMPLES Tell which line is steeper a) Line 1: through (1, -4), (5, 2) Line 2: through (-2, -5), (1, -2) b) Line 1: through (-1, -3), (-3, -2) Line 2: through (3, -4), (0, -3)

S LOPES OF P ARALLEL AND P ERPENDICULAR L INES Parallel Lines have the same slope Perpendicular Lines have slopes that are negative reciprocals of each other

E XAMPLES Tell whether the lines are parallel, perpendicular, or neither a) Line 1: through (1, -2), (3, -2) Line 2: through (-5, 4), (0, 4) b) Line 1: through (-2, -2), (4, 1) Line 2: through (-3, -3), (1, 5)

E XAMPLE Which line is perpendicular to the line through (-3, 1) and (4, -2) Line 1: through (4, -3) and (1, 4) Line 2: through (-3, -3) and (0, 4)

E XAMPLE The slope of a road, or grade, is usually expressed as a percent. For example, if a road has a grade of 3%, it rises 3 feet for every 100 feet of horizontal distance. a) Find the grade of a road that rises 75 feet over a horizontal distance of 2000 feet. b) Find the horizontal length x of a road with a grade of 4% if the road rises 50 feet over its length.

E XAMPLE A water park slid drops 8 feet over a horizontal distance of 24 feet. Find its (positive) slope. Then find the drop over a 54 foot section with the same slope.

E XAMPLE The number of U.S. cell phone subscribers increased from 16 million in 1993 to 44 million in Fin the average rate of change and use it to estimate the number subscribers in 1997.

E XAMPLE The average local monthly U.S. cell phone bill decreased from $61.48 in 1993 to $47.70 in Find the average rate of change and use it to estimate the average monthly bill in 1997.