5.6 Parallel & Perpendicular Lines

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5.6 Parallel & Perpendicular Lines

  1. 1. 5.6 Parallel & Perpendicular Lines
  2. 2. 1. Parallel lines have the same slope <ul><li>Slope of Line A = </li></ul><ul><li>Slope of Line B = </li></ul><ul><li>Slope of Line A = </li></ul>Line A Line B 1 1 Slope of Line B
  3. 3. 2. Perpendicular lines slope at 90° <ul><li>Slope of Line A = </li></ul><ul><li>Slope of Line B = </li></ul><ul><li>Slope of Line A = </li></ul>Line A Line B 1 -1 Opposite Reciprocal of Line B
  4. 4. Write an equation in slope-intercept form for the line parallel to each line below with a y-intercept of 3 . <ul><li>Y = 4x + 2 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>M = _________ </li></ul><ul><li>Step 2: Write equation </li></ul><ul><li>Y = mx + b </li></ul><ul><li>Y = ___x + _____ </li></ul>
  5. 5. Write an equation in slope-intercept form for the line parallel to each line below with a y-intercept of 3. <ul><li>4. Y = -3x - 2 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>M = _________ </li></ul><ul><li>Step 2: Write equation </li></ul><ul><li>Y = mx + b </li></ul><ul><li>Y = ___x + _____ </li></ul>
  6. 6. 6. Find a perpendicular slope of the following slopes. <ul><li>6. Slope = 1/2 </li></ul><ul><li>Perpendicular Slope = _______ </li></ul>
  7. 7. 7. Find a perpendicular slope of the following slopes. <ul><li>7. Slope = 5/6 </li></ul><ul><li>Perpendicular Slope = _______ </li></ul>
  8. 8. 8. Find a perpendicular slope of the following slopes. <ul><li>8. Slope = -4 </li></ul><ul><li>Perpendicular Slope = _______ </li></ul>
  9. 9. Find the slope of a line that is perpendicular to the following lines. <ul><li>9. Y = 3x + 2 </li></ul><ul><li>Slope = _______ </li></ul><ul><li>Perpendicular Slope = __________ </li></ul>
  10. 10. Find the slope of a line that is perpendicular to the following lines. <ul><li>10. 3x + 12y = 12 </li></ul><ul><li>Slope = _______ </li></ul><ul><li>Perpendicular Slope = __________ </li></ul>
  11. 11. Write an equation in point-slope form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. <ul><li>Y = 2x + 3 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>Slope = _______ </li></ul><ul><li>Perpendicular Slope = ______ </li></ul><ul><li>Step 2: Write Equation </li></ul><ul><li>y – y 1 = m (x – x 1 ) </li></ul><ul><li>y - ___ = ___(x -____) </li></ul><ul><li>__________________________ </li></ul>
  12. 12. Write an equation in point-slope form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. <ul><li>3x + y = 7 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>Slope = _______ </li></ul><ul><li>Perpendicular Slope = ______ </li></ul><ul><li>Step 2: Write Equation </li></ul><ul><li>y – y 1 = m (x – x 1 ) </li></ul><ul><li>_________________________ </li></ul><ul><li>__________________________ </li></ul>
  13. 13. Write an equation in slope-intercept form that is perpendicular to the given line. <ul><li>15. (-3, -5), y = 3x - 1 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>Slope (m) = _______ </li></ul><ul><li>Perpendicular Slope = __ </li></ul>Step 2: Write Equation Y = mx + b _____ = _____(____) + b b = _______________
  14. 14. 15. Write an equation in slope-intercept form that is perpendicular to the given line. <ul><li>M = -1/3 </li></ul><ul><li>b = -6 </li></ul><ul><li>Y = mx + b </li></ul><ul><li>Y = ____x + ______ </li></ul>
  15. 15. Write an equation in slope-intercept form that is perpendicualr to the given line. <ul><li>16. (5, 4) y - 10 = -5 x </li></ul><ul><li> 2 </li></ul><ul><li>Step 1: Identify Slope </li></ul><ul><li>Slope (m) = _______ </li></ul><ul><li>Perpendicular Slope = __ </li></ul>Step 2: Write Equation Y = mx + b _____ = _____(____) + b b = _______________
  16. 16. 16. Write an equation in slope-intercept form that is perpendicular to the given line. <ul><li>M = 2/5 </li></ul><ul><li>b = 2 </li></ul><ul><li>Y = mx + b </li></ul><ul><li>Y = ____x + ______ </li></ul>

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