2. 6.6 Warm-up Objective 3 The graph of which function is shown ?
a. Y = 30x
b. Y = 30 - x
c. Y = 30 - (x+5)
d. y = x y 30 20 10 x
Pardekooper

3. 6.6 Warm-up Objective 3 The graph of which function is shown ?
a. Y = 30x
b. Y = 30 - x
c. Y = 30 - (x+5)
d. y = x y 30 20 10 x
Pardekooper

4. Parallel &
Perpendicular Lines
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5. What you’ll learn
To determine if two lines are parallel or perpendicular by their slopes, and
To write equations of lines that pass through a given point, parallel or perpendicular to the graph of the given equation
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6. Here are some terms.
Two lines are parallel if and only if they have the same slope.
example:
Two lines are perpendicular if and only if their slopes are opposite inverses.
example:
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7. Is the following set of lines parallel or perpendicular?
Lets try some.
Is the following set of lines parallel or perpendicular?
y=2x+3
y=2x-5
parallel
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8. Is the following set of lines parallel or perpendicular?
Lets try some.
Is the following set of lines parallel or perpendicular?
y=1/2x+3
y= -2x-5
perpendicular
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9. Is the following set of lines parallel or perpendicular?
Lets try some.
Is the following set of lines parallel or perpendicular?
y=1/4x+1
y=4x-1
neither
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10. Where do the equations come from?
Write the equation for the that is parallel to y=5x-1 with y-intercept of 2.
m=5
b=2
y=mx+b
y=5x+2
Pardekooper

11. Where do the equations come from?
Write the equation for the that is parallel to y=2/3x-1 with y-intercept of -1.
m=2/3
b=-1
y=mx+b
y=2/3x-1
Pardekooper

12. Where do the equations come from?
Write the equation for the that is perpendicular to y=2/3x-1 with y-intercept of -4.
m=-3/2
b=-4
y=mx+b
y=-3/2x-4
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13. Where do the equations come from?
Write the equation for the that is perpendicular to y=-1/4x-1 with y-intercept of 5.
m=4/1
b=5
y=mx+b
y=4x+5
Pardekooper

14. Where do the equations come from?
Write an equation for a line that passes through the point (1,3)and is parallel to y=2x+4.
m=2
P(1,3)
y-y1=m(x-x1)
y-3=2(x-1)
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15. Where do the equations come from?
Write an equation for a line that passes through the point (2,-4)and is parallel to y=2/3x+4.
m=2/3
P(2,-4)
y-y1=m(x-x1)
y-(-4)=2/3(x-2)
Pardekooper

16. Where do the equations come from?
Write an equation for a line that passes through the point (1,-3)and is perpendicular to y=2/3x+1.
m=-3/2
P(1,-3)
y-y1=m(x-x1)
y-(-3)=-3/2(x-1)
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17. Why do we need to know if lines are parallel or perpendicular ?
Given a pair of opposite sides of a quadrilateral are parallel, what does the quadrilateral look like ?
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18. Why do we need to know if lines are parallel or perpendicular ?
Given a pair of opposite sides of a quadrilateral are parallel and equal in length,what does the quadrilateral look like ?
Given a pair of opposite sides of a quadrilateral are parallel, what does the quadrilateral look like ?
In order to know which one, you need more information.
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19. Why do we need to know if lines are parallel or perpendicular ?
Given a pair of opposite sides of a quadrilateral are parallel and equal in length, and a pair of adjacent sides form a right angle,what does the quadrilateral look like ?
Given a pair of opposite sides of a quadrilateral are parallel and equal in length,what does the quadrilateral look like ?
We need some more information.
Pardekooper

20. 3.7 Slopes of Parallel and Perpendicular Lines
Geometry
3.7 Slopes of Parallel and Perpendicular Lines
Are the lines parallel, perpendicular or neither
1. y = -5x 2. y=3x y=1/2x-4
y = 5x y=-1/3x y=1/2x+4
Write an equation for a line that passes through the point and is parallel to the given equation.
4. (2,-7), y = x (1,-2), y = -2x (2,-1), y = -0.5x + 2
Write an equation for a line that passes through the point and is perpendicular to the given equation.
7. (6,-2), y = 3/5x (3,7), y = 3/4x -1
9. Write an equation of the line that has an y-intercept of 3 and is perpendicular to the graph of
5x - 3y = 2.
10. Use slope to show that opposite sides of hexagon RSTUVW are parallel.
11. Use slope to determine whether a triangle with vertices G(3,2), H(8,5), and K(0,10) is a right triangle. R S W T V U