2.2 – Slope and Rate of Change
SLOPE The ratio of vertical change to horizontal change. This only applies to lines and they can not be vertical. Slope is represented by the letter m. The only thing you need at the very least to determine slope is 2 points.
The Slope of a Line ; given and
Worked Out Example Find the slope of a line passing through (-2, -4) and (3, -1) 1. Label numbers 2. Substitute into equation and solve **You always want to leave slope as a fraction, because it is a ratio/a comparison of change!
Find the slope of the line passing through the following points. 1. (1, -5) and (-2, 3) 2. (4, 2) and (-8, 2) 3. ( 8, 4) and (8, 1)
Activity on Properties of Slope Slope Activity
Classifying Lines by their Slope SLOPEGRAPH PositiveRises (left to right) NegativeFalls (left to right) ZeroHorizontal UndefinedVertical
Determine if the graph rises, falls, is horizontal, or vertical without graphing it. 1. (-2, 3) and (1, 5) 2. (1, -2) and (3, -2) 3. (-1, -4) and (6, -5)
Parallel & Perpendicular Lines Parallel Lines: two distinct nonvertical lines are parallel if and only if their slopes are equal. (all vertical lines are parallel to each other) Perpendicular Lines: two nonvertical lines are perpendicular if and only if their slopes are opposite reciprocals of each other. (a vertical line and a horizontal line are always perpendicular to each other)
Determine if the lines passing through the points are parallel, perpendicular, or neither. 1. Line 1: (-1, 9) and (-6, -6) Line 2: (-7, -23) and (0, -2) 2. Line 1: (4, -3) and (-8, 1) Line 2: (5, 11) and (8, 20) 3. Line 1: (-6, 4) and (12, 4) Line 2: (1, -3) and (1, 6)
(Average) Rate of Change The real-life version of slope. Used to describe how something changes over time and to predict the future. Also used to describe how height changes over a horizontal distance Examples: Speed- 50 mph, The grade of a hill – 23%
Cell Phones The number of U.S. cell phone subscribers increased form 16 million in 1993 to 44 million in Find the average rate of change and use it to estimate the number of subscribers in 1997.
Leaning Tower of Pisa The top of the Leaning Tower of Pisa is about 55.9 meters above the ground. As of 1997 its top was leaning about 5.2 meters off-center. Approximate the slope of the tower.
Grand Canyon You are camping at the Grand Canyon. Why you pitch your tent at 1:00 PM, the temperature is 81°F. When you wake up at 6:00 AM, the temperature is 47°F. What is the average rate of change in the temperature? Estimate the temperature when you went to sleep at 9:00 PM.
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