Transcript BEI06_ppt_0303

Chapter 3
Introduction to
Graphing
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3.3 Graphing and Intercepts
• Intercepts
• Using Intercepts to Graph
• Graphing Horizontal or Vertical Lines
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Example
For the graph shown below, a) give the coordinates
of any x-intercepts and b) give the coordinates of
any y-intercepts.
Solution
a) The x-intercepts are
(2, 0) and (2, 0).
b) The y-intercept is
(0, -4).
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To Find Intercepts
To find the y-intercept(s) of an equation’s
graph, replace x with 0 and solve for y.
To find the x-intercept(s) of an equation’s
graph, replace y with 0 and solve for x.
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Example
Find the y-intercept and the x-intercept of the graph of
5x + 2y = 10.
Solution
To find the y-intercept, we let x = 0 and solve for y:
Replacing x with 0
5 • 0 + 2y = 10
2y = 10
y=5
The y-intercept is (0, 5).
To find the x-intercept, we let y = 0 and solve for x.
Replacing y with 0
5x + 2• 0 = 10
5x = 10
x=2
The x-intercept is (2, 0).
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Example
Graph 5x + 2y = 10 using intercepts.
Solution
We found the intercepts in the
previous example. Before
drawing the line, we plot a third
point as a check.
If we let x = 4, then
5 • 4 + 2y = 10
20 + 2y = 10
2y = 10
y = 5
We plot (4, 5), (0, 5) and (2, 0).
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y-intercept (0, 5)
x-intercept (2, 0)
5x + 2y = 10
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Example
Graph 3x  4y = 8 using intercepts.
Solution
To find the y-intercept, we let x = 0. This amounts to ignoring
the x-term and then solving.
4y = 8
y = 2
The y-intercept is (0, 2).
To find the x-intercept, we let y = 0. This amounts to ignoring
the y-term and then solving.
3x = 8
x = 8/3
The x-intercept is (8/3, 0).
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Example
continued
Find a third point.
If we let x = 4, then
3 • 4  4y = 8
12  4y = 8
4y = 4
y=1
We plot (0, 2); (8/3, 0);
and (4, 1).
x-intercept
y-intercept
3x  4y = 8
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Example
Graph: y = 2
Solution
We regard the equation y = 2 as 0 • x + y = 2. No matter
what number we choose for x, we find that y must equal 2.
y=2
Choose any number for x.
x
0
4
4
y
2
2
2
(x, y)
(0, 2)
(4, 2)
(4 , 2)
y must be 2.
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Example
When we plot the ordered
pairs (0, 2), (4, 2) and
(4, 2) and connect the
points, we obtain a
horizontal line.
y=2
(0, 2)
(4, 2)
(4, 2)
Any ordered pair of the form
(x, 2) is a solution, so the
line is parallel to the x-axis
with y-intercept (0, 2).
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Example
Graph x = 2
Solution
We regard the equation x = 2 as x + 0 • y = 2. We
make up a table with all 2 in the x-column.
x = 2
x must be 2.
x
2
2
2
y
4
1
4
(x, y)
(2, 4)
(2, 1)
(2, 4)
Any number can be used for y.
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Example
Solution
When we plot the ordered
pairs (2, 4), (2, 1), and
(2, 4) and connect them,
we obtain a vertical line.
Any ordered pair of the form
(2, y) is a solution. The line
is parallel to the y-axis with
x-intercept (2, 0).
x = 2
(2, 4)
(2, 1)
(2, 4)
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Example
Write an equation for the
graph.
Solution
Note that every point on
the horizontal line passing
through (0, 3) has 3 as
the y-coordinate.
The equation of the line is
y = 3.
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Example
Write an equation for
the graph.
Solution
Note that every point on
the vertical line passing
through (4, 0) has 4 as
the x-coordinate.
The equation of the line
is x = 4.
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