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Parallel & Perpendicular Lines

Parallel & Perpendicular Lines. Parallel Lines have the same Slope (or same Rise/Run). Finding the Slope of a Line Parallel to another Line is a No Brainer. Find the slope of a line Parallel to y=3x+5. Slopes of Parallel Lines. Find the slope of a line Parallel to y=3x+5.

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Parallel & Perpendicular Lines

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  1. Parallel & Perpendicular Lines

  2. Parallel Lines have the same Slope(or same Rise/Run)

  3. Finding the Slope of a Line Parallel to another Line is aNo Brainer

  4. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines

  5. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines 1. Solve the equation for y.

  6. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines Solve the equation for y. (Already done in this case) y=3x+5 Ans. Is 3 This puts the equation in Slope intercept form so Slope is # in front of x.

  7. Find the slope of a line Parallel to y=2x+9 Slopes of Parallel Lines Solve the equation for y.

  8. Find the slope of a line Parallel to y=2x+9 Slopes of Parallel Lines Solve the equation for y. Solve the equation for y. (Already done in this case) y=2x+9 Ans. Is 2

  9. Find the slope of a line Parallel to 2y=8x+16 Slopes of Parallel Lines Solve the equation for y. Solve the equation for y.

  10. Find the slope of a line Parallel to 2y=8x+16 Slopes of Parallel Lines 2y=8x+16 Solve the equation for y. Solve the equation for y. 2 2 2 y=4x+8 Ans. Is 4

  11. Find the slope of a line Parallel to: 1.

  12. Find the slopes of a line Parallel to: 1. ANSWERIS 9/5

  13. Find the slopes of a line Parallel to: 4. 5. 2. 6. 3.

  14. Find the slopes of a line Parallel to: 4. 5. 2. 4 4 4 3.

  15. Solve the equation for y. 6. +3 +3 -1 -1 -1

  16. Given the equation of one line y=1/2x+1 •(0,1)

  17. Find the equation of a parallel line through a point y=1/2x+1 •(2,-1)

  18. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines

  19. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines Slope Is 3 Solve the equation for y to find slope. (Already done in this case) y=3x+5 y=3x+5

  20. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines x y Slope Is 3 Solve the equation for y to find slope. Put slope & (x,y) point into y=mx+b to find b. y=3x+5 y=3x+5 3=3(4)+b 3=12+b -9=b -12 -12

  21. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines x y Slope Is 3 Solve the equation for y to find slope. Put slope & (x,y) point into y=mx+b to find b. Put m&b (from steps 1&2) into y=mx+b To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK) 1. y=3x+5 3=3(4)+b 3=12+b -9=b 2. -12 -12 3. y=3x-9

  22. Find the eq. of a line Parallel to y=-2x+6 and Through Point (5,1) Equations of Parallel Lines Solve the equation for y to find slope. Put slope & (x,y) point into y=mx+b to find b. Put m&b (from steps 1&2) into y=mx+b

  23. Find the equation of a line Parallel to given line and through Pt: 1. (4,-2) 2. (-3,-6) 3. (5,8)

  24. Slopes of Perpendicular Lines NEG RECIPROCAL (Double Switch)

  25. (6,4) Perpendicular Line 4 • 3 2 -3 (3,2) 2 • 3 2 1 (0,0) 2 1 3 4 5 6

  26. How to remember Perpendicular Lines have NEG-RECIPROCAL Slopes ???

  27. How to remember Perpendicular Lines have NEG-RECIPROCAL Slopes One slope is positive up the mountian the other one is negative down the mountian.

  28. Perpendicular Lines have NEG-RECIPROCAL Slopes 2/3 is to -3/2

  29. What is the NEG-RECIPROCAL 1.

  30. What is the NEG-RECIPROCAL 1. -3 2

  31. What is the NEG-RECIPROCAL 2.

  32. What is the NEG-RECIPROCAL 3 2. 5

  33. What is the NEG-RECIPROCAL 3.

  34. What is the NEG-RECIPROCAL 3. 8 7

  35. What is the NEG-RECIPROCAL 4.

  36. What is the NEG-RECIPROCAL 4. -1 7

  37. What is the NEG-RECIPROCAL 5. 6.

  38. What is the NEG-RECIPROCAL 1 5. 10 6. 5 9

  39. Solving for the equation of a line perpendicular to another line & through the point (0,-3). • (0,-3) Given line y=x+3

  40. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines

  41. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines 1. Solve the equation for y.

  42. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines y=3x+5 Solve the equation for y. (Slope is Neg. Reciprocal) Perpendicular slope is -1/3

  43. Find the slope of a line Perpendicular to y=2x+9 Slopes of Perpendicular Lines Solve the equation for y.

  44. Find the slopes of a line Perpendicular to: 4. 1. 5. 2. 6. 3.

  45. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines

  46. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines Slope Is 3 Neg Recip Is -1/3 Solve the equation for y to find slope. (Slope is Neg. Reciprocal) y=3x+5 y=3x+5

  47. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines x y Slope Is 3 Neg Recip Is -1/3 Solve the equation for y to find slope. (Use Neg Recip) Put slope & (x,y) point into y=mx+b to find b. y=3x+5 y=3x+5 +4/3 +4/3

  48. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines x y Slope Is 3 Neg Recip Is -1/3 Solve the equation for y to find slope. (Use Neg Recip) Put slope & (x,y) point into y=mx+b to find b. Put m&b (from steps 1&2) into y=mx+b To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK) y=3x+5 +4/3 +4/3

  49. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines x y Slope Is -2 Neg Recip Is 1/2 Solve the equation for y to find slope. (Use Neg Recip) Put slope & (x,y) point into y=mx+b to find b. y=-2x+6 -5/2 -5/2

  50. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines

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