Lines
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Warm-up
1. What is the formula for the slope of a line?
2. Find the slope of the line that goes through (-2, 0) and (3, 1).
3. Find the slope of the line that goes through (-1, 2) and (2, 2)
Three Equivalent Ways to Think of Slope
1.
2.
3.
The Slope of a Line
1. A line with positive slope _________________ from left to right.
2. A line with negative slope ________________ from left to right.
3. A line with a slope of zero is ____________________ .
4. A line with undefined slope is ____________________ .
Example 1
a) Find the slope of the line that goes through (4, -2) and (4, 5).
b) Graph the points from part a and draw the line that goes through them.
Lines
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The Point-Slope Form of the Equation of a Line
This form is useful for ____________________________________________________________________ .
y  y1  m(x  x1)
1. What do x and y stand for?
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2. What does m stand for?
3. What do x1 and y1 stand for?
Example 2
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Find an equation of the line that passes through the point (-1, 2) and has a slope of 3.
Practice Problem 2
Find an equation of the line that passes through the point (0, -2) and has a slope of 3.
Slope-Intercept Form of the Equation of a Line
This form is useful for __________________________________________________________________ .
y  mx  b
What does x stand for?
 What does y stand for?
What does m stand for?
What does b stand for?
Lines
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Example 3
Put the following equation in slope-intercept form, give the slope and y-intercept,
and then graph the line.
x y 2
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Example 4
Put the following equation in slope-intercept form, give the slope and y-intercept,
and then graph the line.
y4
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Practice Problem 4
Put the following equation in slope-intercept form, give the slope and y-intercept,
and then graph the line.
x  2y  4
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Summary of Equations of Lines
1.
2.
3.
4.
5.
General Form
Vertical Line
Horizontal Line
Slope-Intercept Form
Point-Slope Form
Parallel and Perpendicular Lines
1. Parallel Lines have ______________________________ slopes.
2. Perpendicular lines have _______________________________ slopes.
Lines
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Example 5
Find the equation of the line that passes through (2, -1) and is parallel to the line
2x  3y  5
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Example 6
Find the equation of the line that passes through (2, -1) and is perpendicular to the
line:
2x  3y  5
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Practice Problem 6
Find the equation of the line that passes through (2, 1) and is
a) parallel to 4x  2y  3
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b) perpendicular to 4x  2y  3
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Lines
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Class Work:
1. Sketch the lines through the point with the indicated slopes on the graph below:
(-4, 1) Slopes: (a) 3
(b) -3 (c) 1/2
2. Find the slope of the line that goes through (2, 4) and (4, -4).
3. Find the equation of the line that passes through the point (-2, -5) with slope
m = ¾. Then graph the line.
4. Find the equation of the line that passes through the point (-10, 4) with slope
m is undefined. Then graph the line.
Lines
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5. Determine the slope and y-intercept of the line 3x  4 y 1. Then graph the line.
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6. Find the slope and y-intercept of the line 11 8y  0 . Then graph the line.
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7. Write an equation of the line that passes through the points (4, 3) and (-4, -4).
8. Write the equation of the lines through the given point (a) parallel to the given
line and (b) perpendicular to the given line.
(2/5, -1), 3x  2y  6
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