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Equations of Parallel & Perpendicular Lines

Learn how to write equations of parallel and perpendicular lines given specific information. Practice with classwork and homework worksheets.

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Equations of Parallel & Perpendicular Lines

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  1. Warmup • Write an equation given the following info: • 1. m = (-9, -1) 2. (-2, -1) (-2, 3) • 3. (-2, 6) (2, 8) 4. m = 0 (3, 4)

  2. Review HW

  3. PARALLEL LINES • Graphs: Lines Never Intersect and are in the same plane • Equations: • Same Slopes • Different y-intercepts

  4. PERPENDICULAR LINES • Graphs: Lines Intersect at 90º angles • Equations: • Negative Reciprocal Slopes • With the same or different y-int

  5. Find the Negative Reciprocal Slopes

  6. Are these lines parallel, perpendicular, or neither? parallel • y = -2x + 1 • y = -2x – 4 • y = 3x – 4 • y = -3x + 1 • y = 1/5 x + 2 • y = -5x + 6 neither perpendicular

  7. Are these lines parallel, perpendicular, or neither? 4. y = -2x + 1 y = -1/2x – 4 5. y = 3x – 4 y = 1 + 3x 6. y = 5/6 x + 2 y = -6/5 x + 6 neither parallel perpendicular

  8. How to Write an Equation of a LinePARALLEL to another and given a point 1. Given equation should be solved for y (y = mx + b) • Write down the slope of that line • Substitute m and (x, y) into y = mx + b. • Solve for b. • Write the new equation using m and b.

  9. Write a line parallel to the line 2x + y = 3 and passes through the point (-2, 5). y = -2x + 1

  10. Write a line parallel to the line y = 3x – 5 and passes through the point (-5, -2). y = 3x + 13

  11. Write a line parallel to the line y = -4x + 1 and passes through the point (2, -1). y = -4x + 7

  12. Write a line parallel to the line y = -x – 7 and passes through the point (-4, -4). y = -x – 8

  13. How to Write an Equation of a LinePERPENDICULAR to another and given a point 1. Given equation should be solved for y (y = mx + b) • Write down the NEGATIVE RECIPROCAL slope of that line • Substitute m and (x, y) in y = mx +b. • Solve for b. • Write the new equation using m and b.

  14. Write a line perpendicular to the line y = ½ x – 2 and passes through the point (1, 0). y = -2x + 2

  15. Write a line perpendicular to the line y = -3x + 2 and passes through the point (6, 5). y = 1/3x + 3

  16. Write a line perpendicular to the line 2x + 3y = 9 and passes through the point (6, -1). y = 3/2 x – 10

  17. Write a line perpendicular to the line y = 2x – 1 and passes through the point (2, 4). y = -1/2x + 5

  18. Write a line perpendicular to the line and passes through the point (5, 1). y = 3x – 14

  19. Classwork Worksheet 12 problems

  20. Homework Worksheet – 13 problems Equations of Parallel & Perpendicular Lines

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