Parallel and Perpendicular Lines
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Transcript of Parallel and Perpendicular Lines
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Parallel and Perpendicular Lines
Please get your Composition books out and be ready to take notes.
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How can we find a line Parallel to another line?
First, Lets Visualize parallel lines What do they
have in common?
Slope! What is
different? x- and y-ints!
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So What do parallel lines share?
The same slope!
Slope = 1
Slope = 1
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Finding a parallel line to any line.
Step 1: Find the Slope (m) Step 2: write another equation with
that same slope. Step 3: Bob is your uncle! You’ve done
it.
Now You Try!
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Find a parallel Line to this equation:
Y = 7x – 12
Stumped? There are tons!! Check it out.
Y = 7x + 4
Y = 7x + 1/9Y = 7x + 2
Y = 7x - 2
Y = 7x + 3.1415926
Y = 7x – 1.44Y = 7x + 1000
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Find a parallel Line to this equation through the point (6,-1):
y = 5x + 3
Now since it’s through a point, then it will have a specific y-int (b). We know m=5, so lets solve for b.
y = 5x + b -1 = 5(6) + b -1 = 30 + b -30 -30 -31 = b
So our equation would be:
Y = 5x - 30
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Find a parallel Line to this equation through the point (3,-2):
x = 5
This line is horizontal, a horizontal line going though point (3,-2) will be parallel.
What would that line be?
x = 3!
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How Can we find a line perpendicular line to another line?
First, Lets Visualize perpendicular lines This isn’t so
straight forward. Looking at the
blue line, what is it’s slope?
2 How about the
red line? -1/2
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Quickly, what is reciprocal? It is a number you multiply by that gets
you to 1. For example 5. What times 5 will equal 1? 1/5 Don’t believe me? Try it 5(1/5) = 1
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Opposite Reciprocal of Slope
If Slope = m, Then the opposite reciprocal would be…
1m
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Perpendicular Lines are cool
Perpendicular Lines!
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How Can we find a line perpendicular line to another line?
So, to find a perpendicular line to another line, the slope is opposite and reciprocal.
What is the Opposite Reciprocal of 4? -1/4 How about 1/3? -3 How about -1/8? 8
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Finding a perpendicular line to any line.
Step 1: Find the Slope (m) Step 2: Find the opposite reciprocal = -1/m
Step 3: Bob is your uncle! You’ve done it.
Now You Try!
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Find a perpendicular Line to this equation:
Y = 7x – 12
Stumped? There are tons!! Check it out.
Y = (-1/7)x + 4Y = (-1/7)x + 1/3
Y = (-1/7)x + 5Y = (-1/7)x - 8 Y = (-1/7)x + 444
Y = (-1/7)x – 1.44
Y = (-1/7)x + 10,000
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Find a perpendicular Line to this equation through the point (5,-2):
y = 5x + 3
opposite reciprocal = -1/m -1/5, Now lets find b.
y = (-1/5)x + b -2 = (-1/5)(5) + b -2 = -1 + b +1 +1 -1 = b
So our perpendicular equation would be:
Y = (-1/5)x - 1