5.3.1 Slope of a Line
The measure of a line’s slant is called the slope of the line, denoted
m. The slope of a non-vertical line containing the two points
and 
is
given by
Figure 1 Slope of a line,
Example 1
a. Graph the line containing the two
points (-2, 4) and (8, -1). Then
compute the slope of the line.
b. Pick two other points on the line in
part a and compute the slope of the
line using those two points.
c. A line that falls from left to right is called a decreasing line.
Decreasing lines have a slope that is [ positive negative ]. |
 |
Example 2
a. Graph the line containing the two
points (-5, - 5) and (7, 3). Then
compute the slope of the line.
b. A line that rises from left to right is
called an increasing line. Increasing
lines have a slope that is [positive
negative]. |
|
Example 3
a. Graph the line containing the two
points (6, 4) and (6,1). Then compute
the slope of the line.
b. Vertical lines have a slope that is
[positive negative zero undefined].
c. List three other ordered -pairs on the
line.
d. What is the equation of the line ? |
|
Example 4
a. Graph the line containing the two
points (-7, - 5) and (1, - 5). Then
compute the slope of the line.
b. Horizontal lines have a slope that is
[positive negative zero undefined ].
c. List three other ordered-pairs on the
line.
d. What is the equation of the line? |
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Example 5
a. Graph the line containing the two points
(6, 3) and (-2, 7). Then compute the
slope of the line.
b. Graph the line containing the two points
(6, -1) and (2,1). Then compute the
slope of the line.
c. What can be said about the two lines
from parts a and b? |
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5.3.2 Slopes of Parallel and Perpendicular Lines
Slopes of Parallel lines
Two non-vertical lines are parallel if and only if their slopes are
equal. The preceding statement is equivalent to the following three:
1. If two non-vertical lines are parallel, then their slopes are equal.
2. If two non-vertical lines have equal slopes, then they are parallel.
3. All vertical lines are parallel.
Slopes of Perpendicular lines
Two lines are perpendicular if and only if their slopes are opposite
reciprocals of each other. That is, if two lines
and 
have
slopes
and 
,
respectively, then the preceding statement is equivalent to
the fol lowing three :
1. If is perpendicular to
, then
.
2. If
, then
is perpendicular to .
3. Every horizontal line is perpendicular to every vertical line.
Example 6
For each slope given,
fill-in the table
with the slope of every
line parallel to and
perpendicular to a line
with the given slope. |
| Slope |
Slope of any
parallel line |
Slope of any
perpendicular
line |
 |
| undefined |
|
|
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Example 7
a. Graph the line containing the two
points (6, 3) and (-2, 7). Then
compute the slope of the line.
b. Graph the line containing the two
points (-2, - 3) and (3, 7). Then
compute the slope of the line.
c. What can be said about the two
lines from parts a and b? |
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5.3.2 Graph a line using the slope and y-intercept
Slope- Intercept Form of a Straight Line
|
The Slope-Intercept Form of a Straight Line is
given by y = mx + b, |
where the slope of the line is m and the y-intercept
is (0, b).  |
| |
 |
Example 1 Identify the slope and y-intercept in the
graph of each
equation.
| Equation, y = mx + b |
Slope = m |
y-intercept, (0, b) |
 |
Example 2 Graph
y = 2x - 3 using the
slope and y-intercept.
i. Identify the slope and y-intercept.
ii. Plot the y -intercept.
iii. Use the slope,  , to
generate
other points on the line. |
|
Example 3 Use the slope and y-intercept
to graph
 |
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Example 4 Use the slope and y-intercept
to graph
 |
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Example 5 Use the slope and y-intercept
to graph
y = 3x + 5. |
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