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Chapter 3
Introduction to
Graphing
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3.6
Slope-Intercept Form
• Using the y-intercept and the Slope to Graph a
Line
• Equations in Slope-Intercept Form
• Graphing and Slope-Intercept Form
• Parallel and Perpendicular Lines
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Example
Draw a line that has slope 2/3
and y-intercept (0, 1).
Solution
We plot (0, 1) and from there
move up 2 units and to the right
three units. This locates the point
(3, 1).
right 3
up 2
(0, 1)
(3, 1)
y-intercept
We plot the point and draw a line
passing through the two points.
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The Slope-Intercept Equation
The equation y = mx + b is called
the slope-intercept equation.
The equation represents a line of
slope m with y-intercept (0, b).
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Example
Find the slope and the y-intercept of each line
whose equation is given.
a) y  3 x  2
b) 3x + y = 7 c) 4x  5y = 10
8
Solution
a) y  3 x  2
8
3
The slope is
. The y-intercept is (0, 2).
8
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Example
b) We first solve for y to find an equivalent form of
y = mx + b.
3x + y = 7
y = 3x + 7
The slope is 3. The y-intercept is (0, 7).
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Example
c) We rewrite the equation in the form y = mx + b.
4x  5y = 10
5 y  4 x  10
1
y    4 x  10 
5
4
y  x2
5
The slope is 4/5. The y-intercept is (0, 2).
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Example
A line has slope 3/7 and y-intercept (0, 8). Find an
equation of the line.
Solution
We use the slope-intercept equation, substituting
3/7 for m and 8 for b:
y  mx  b
3
y   x  8.
7
3
The desired equation is y   x  8.
7
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3-8
Example
4
Graph: y  x  2
3
Solution
The slope is 4/3 and the
y-intercept is (0, 2).
We plot (0, 2), then move
up 4 units and to the right 3
units.
We could also move down
4 units and to the left 3
units.
Then draw the line.
right 3
(3, 2)
up 4 units
(0, 2)
y
4
x2
3
down 4
(3, 6)
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left 3
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Example
Graph: 3x + 4y = 12
Solution
Rewrite the equation in slope-intercept form.
3 x  4 y  12
4 y  3x  12
1
y   3 x  12 
4
3
y   x3
4
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Example
Solution
The slope is 3/4 and
the y-intercept is (0, 3).
We plot (0, 3), then
move down 3 units and
to the right 4 units.
An alternate approach
would be to move up 3
units and to the left 4
units.
left 4
(4, 6)
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up 3
(0, 3)
down 3
right 4 (4, 0)
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Parallel and Perpendicular Lines
Two lines are parallel if they lie in the same
plane and do not intersect no matter how far
they are extended.
Two lines are perpendicular if they intersect at
a right angle. If one line is vertical and another
is horizontal, they are perpendicular.
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Slope and Parallel Lines
Two lines are parallel if they have the
same slope or if both lines are vertical.
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Example
3
Determine whether the graphs of y  x  3
2
and 3x  2y = 5 are parallel.
Solution
Remember that parallel lines extend indefinitely
without intersecting. Thus, two lines with the same
slope but different y-intercepts are parallel.
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Example
3
The line y  x  3 has slope 3/2 and y-intercept 3.
2
We need to rewrite 3x  2y = 5 in slope-intercept
form:
3x  2y = 5
2y = 3x  5
3
5
y  x
2
2
The slope is 3/2 and the y-intercept is 5/2.
Both lines have slope 3/2 and different y-intercepts,
the graphs are parallel.
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Slope and Perpendicular Lines
Two lines are perpendicular if the product of
their slopes is –1 or if one line is vertical and
the other is horizontal.
Thus, if one line has slope m (m  0), the
slope of a line perpendicular to it is –1/m.
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Example
Determine whether the graphs of 2x + y = 10 and
1
y  x  9 are perpendicular.
2
Solution
Write the first equation in slope-intercept form.
2 x  y  10
y  2 x  10
The slope of the second line is 1/2.
The lines are perpendicular the product of their
slopes is –1.
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