Chapter 2.2
The Slope of a line
College Algebra
by Example Series
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Chapter 2.2
The Slope of a line
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College Algebra by Example Series |
Key Concept: Understand how to interpret and determine the slope
or rate of change of functions within the
rectangular coordinate system.
Skills to Learn:
1. Know how to find the slope given any two points on a graph
2. Know how to determine non-vertical slopes of lines
3. Know how to determine the slopes of parallel and perpendicular lines
4. Know how to find the slope in real world application problems
| The Slope,
m (rate of change of) of a non vertical line passing through any two
points P(x1, y1) and Q(x2, y2)
is defined as the rate of change of y with respect to x:
Example 1. Find slope of line with points: P(-4, -4) and Q(5, 4)
Note x1 is smallest vale of x |
Slope Illustrated
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| Example 2. Find slope
given points (-3, 2) and (4, -4) (slope
is -6/7)
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Example 3. Find slope
of line with these points (0, 3) and (-2, -3) (slope is 3)
First order points: (-2, -3) and (0, 3)
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| Example 4. Slopes of
Horizontal lines = 0: P(-4,
8) and Q(5, 8)
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Example 5. Slopes of
Vertical lines are undefined: P(4,
3) and (4, 8) (slope is Undefined)
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| Example 6. Slopes of
Parallel lines are equal: If
slope of line 1 = 2, then slope of line 2 = 2 also.
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Example 7. Slopes of
Perpendicular lines are negative
reciprocals of each other.
If If
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Examples: Applications
| Example 8. Find the rate
of depreciation of a car from $25,000 in 1992 to $500 in 2002.
Points (time, t, Value, $): (1992, 25000) and (2002, 500)
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Example 9. What is the
service rate of people in a queue if after 10 minutes there are 20 people
serviced and after 18 minutes 35 serviced?
Let P(10, 20) and Q(18, 35)
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1.875 per minute