Download Graphing Lines - Barry University

Graphing Lines
Dr. Carol A. Marinas
Graphing Lines
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Plotting Points on a Coordinate System
Graphing a line using points
Graphing a line using intercepts
Finding the slope
Graphing a line using slope and a point
Graphing a line using slope and y-intercept
Horizontal & Vertical Lines
Parallel & Perpendicular Lines
Equations of a Line
Plotting points on a
coordinate system
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(x, y)
x moves left or right & y moves up or down
(1, 1) is right 1 and up 1
(-2, -1) is 2 to the left and 1 down
Graphing a line using points
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Make a table finding
at least 3 points
Example:
2x + y = 4
x
1
-1
3
y
2
6
-2
Graphing a line using intercepts
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Make a
table
Example:
2x + y = 4
x
0
2
y
4
0
X-intercept put 0 in
for y and solve for x.
2x + 0 = 4
x=2
(2, 0) is x-intercept
 y-intercept put 0 in
for x and solve for y.
 2(0) + y = 4
y=4
(0, 4) is y-intercept
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Finding the slope given
2 points
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m=
y 2  y1
x 2  x1
Find the slope of the
line connecting
(-2,1) and (6, -3)
m = -3 - 1 = -1
6 - (-2)
2
Graphing Using the Slope
and a Point
 Graph the point
 Do the slope from
that point (up/down
for numerator and
left/right for
denominator)
 Follow same pattern
for more points
 Draw the line
Example:
Point (1, -2) & m= 1/3
Graphing line using the slope
and y-intercept
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Graph y-intercept
Do slope (up/down,
left/right)
Draw line
Example:
y-intercept (0, 2)
m = 3/2
Horizontal & Vertical Lines
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y = c where c is a constant
Horizontal line
y-intercept (0, c)
Slope is 0
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x= c where c is a constant
Vertical line
x-intercept is (c, 0)
Slope is undefined or NO
slope
Parallel & Perpendicular Lines
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Parallel lines have
the same slope
Example:
y = 2x + 1
y = 2x -4
Both have a slope of
2, therefore the lines
are parallel
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Perpendicular lines
have slopes whose
product is -1.
Example:
y = 3x + 2
y = -1/3 x - 4
First has slope of 3
and second has a
slope of -1/3.
3 * -1/3 = -1
Equations of a Line
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Ax + By + C = 0 (General Form - no
fractions for A, B, or C)
y = mx + b (Slope - intercept form)
m is the slope and (0, b) is the y-intercept
y - y1 = m (x - x1) (Point - slope form)
(x1, y1) is a point and m is the slope
Questions about Lines
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Find the equation of a line
in GENERAL FORM
through (-2, 2) and (1, 3)
Find the equation of a line
in Slope-intercept form
through (6, -2) and
parallel to 3x - 2y =4
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Find the equation of
the line with a slope
of 0 and a y-intercept
of (0, -3)
Find the equation of a
line in Slope-intercept
form and through
(4, 3) & perpendicular
to 2x = 4y + 6
Answers to Lines
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Find the equation
of a line in
GENERAL FORM
through (-2, 2)
and (1, 3)
Slope = 3 - 2 = 1
1- (-2) 3
Using Point-slope equation:
y - 2 = 1/3 (x - -2)
y - 2 = 1/3 x + 2/3
3y - 6 = x + 2
-x + 3y -8 = 0 OR
x - 3y + 8 = 0
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Answers to Lines
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Find the equation of a
line in Slope-intercept
form through (6, -2)
and parallel to
3x - 2y = 4
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Find the slope of 3x - 2y =
4 by solving for y.
-2y = -3x + 4
y = 3/2 x - 2
m = 3/2 (Parallel lines have the
same slope)
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Using Point-slope equation:
y - (- 2) = 3/2 (x - 6)
y + 2 = 3/2 x - 9
y = 3/2 x - 11
Answers to Lines
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Find the equation of
the line with a slope of
0 and a y-intercept of
(0, -3)
Find the equation of a
line in Slope-intercept
form and through
(4, 3) & perpendicular
to 2x = 4y + 6
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Slope of 0 means this is a
horizontal line in the form y = c.
So y = -3
Find slope of 2x = 4y + 6 by
solving for y. y = 1/2 x - 3/2
Slope of perpendicular line is -2.
(Because 1/2 * -2 = -1)
y - 3 = -2 (x - 4)
y = -2x + 11
Hope you enjoyed Lines !