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May 24th

May 24th

Graphing Linear Equations and Inequalities

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? 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?

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
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?

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 Example 4 Use the slope and y-intercept to graph Example 5 Use the slope and y-intercept to graph y = 3x + 5.
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