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Parallel and Perpendicular Lines

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 !.

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Parallel and Perpendicular Lines

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  1. Parallel and Perpendicular Lines Please get your Composition books out and be ready to take notes.

  2. 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!

  3. So What do parallel lines share? • The same slope! Slope = 1 Slope = 1

  4. 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!

  5. Find a parallel Line to this equation: • Y = 7x – 12 Stumped? There are tons!! Check it out. Y = 7x + 4 Y = 7x - 2 Y = 7x – 1.44 Y = 7x + 1000 Y = 7x + 2 Y = 7x + 1/9 Y = 7x + 3.1415926

  6. 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

  7. 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!

  8. 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

  9. 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

  10. Opposite Reciprocal of Slope • If Slope = m, Then the opposite reciprocal would be…

  11. Perpendicular Lines are cool Perpendicular Lines!

  12. 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

  13. 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!

  14. Find a perpendicular Line to this equation: • Y = 7x – 12 Stumped? There are tons!! Check it out. Y = (-1/7)x + 4 Y = (-1/7)x + 1/3 Y = (-1/7)x – 1.44 Y = (-1/7)x + 10,000 Y = (-1/7)x + 5 Y = (-1/7)x - 8 Y = (-1/7)x + 444

  15. 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

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