Download 2.2 * Slope and Rate of Change

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
;
and
given
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
SLOPE
GRAPH
Positive
Rises (left to right)
Negative
Falls (left to right)
Zero
Horizontal
Undefined
Vertical
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.
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)
1.
(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 1996. 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.
Homework
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