Sullivan Algebra and Trigonometry: Section 2'3 Lines

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Sullivan Algebra and Trigonometry Section
2.3Lines

• Objectives
• Calculate and Interpret the Slope of a Line
• Graph Lines Given a Point and the Slope
• Use the Point-Slope Form of a Line
• Find the Equation of a Line Given Two Points
• Write the Equation of a Line in Slope-Intercept
  From and in General Form.
• Identify the Slope and the y Intercept of a Line
  from its Equation.

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Let and be two
distinct points with . The slope m of
the non-vertical line L containing P and Q is
defined by the formula
If , L is a vertical line and the
slope m of L is undefined (since this results in
division by 0).
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Slope can be though of as the ratio of the
vertical change ( ) to the
horizontal change ( ), often termed
rise over run.
y
x
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If , then is zero and
the slope is undefined. Plotting the two points
results in the graph of a vertical line with the
equation .

L
y
x
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Example Find the slope of the line joining the
points (3,8) and (-1,2).
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Some Important Facts about slope
1. When the slope of a line is positive, the line
slants upward from left to right. (L1)
2. When the slope of a line is negative, the line
slants downward from left to right. (L2)
3. When the slope is zero, the line is
horizontal. (L3)
4. When the slope is undefined, the line is
vertical. (L4)
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Example Draw the graph of the line passing
through (1,4) with a slope of -3/2.
Step 1 Plot the given point. Step 2 Use the
slope to find another point on the line (vertical
change -3, horizontal change 2).
y
2
(1,4)
-3
(3,1)
x
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Example Draw the graph of the equation x 2.
y
x 2
x
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Theorem Point-Slope Form of an Equation of a Line
An equation of a non-vertical line of slope m
that passes through the point (x1, y1) is
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Example Find an equation of a line with slope -2
passing through (-1,5).
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A horizontal line is given by an equation of the
form y b, where (0,b) is the y-intercept.
Example Graph the line y4.
y 4
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Example Find the slope m and y-intercept (0,b)
of the graph of the line 3x - 2y 6 0.