Parallel and Perpendicular Lines

Please get your Composition books out and be ready to take notes.

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!

So What do parallel lines share?

The same slope!

Slope = 1

Slope = 1

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!

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

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

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!

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

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

Opposite Reciprocal of Slope

If Slope = m, Then the opposite reciprocal would be…

1

m

Perpendicular Lines are cool

Perp

en

dic

ula

r Lin

es!

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

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!

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 + 5

Y = (-1/7)x - 8 Y = (-1/7)x + 444

Y = (-1/7)x – 1.44

Y = (-1/7)x + 10,000

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