Module 5 topic 2
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Module 5 topic 2 Module 5 topic 2 Presentation Transcript

  • Module 5 Topic 2
    Parallel and Perpendicular Slopes
  • Example 1
    Similar Problem: If line one has a slope of 3, what does the slope of line 2 need to be if the lines are perpendicular?
    Remember that perpendicular slopes are the opposite reciprocals so if we have 3 then the opposite reciprocal would be -1/3
  • Example 2
    Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?
    x + 4y = 7 (solve for y)
    4y = -x + 7
    y = -x/4 + 7/4
    remember that -x/4 the slope is -1/4 so the parallel slope is also -1/4
  • Example 3
    Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?
    x + 4y = 7 (solve for y)
    4y = -x + 7
    y = -x/4 + 7/4
    remember that -x/4 the slope is -1/4 so the perpendicular slope is the opposite reciprocal which would be 4/1 or 4
  • Example 4
    Similar Problem: Write the slope-intercept equation of the line perpendicular to y = 7/2 x - 2, which passes through the point (0, 3).
    y = 7/2 x - 2 (the slope is 7/2 so the perpendicular slope is -2/7)
    Use the perpendicular slope and the ordered pair to find b in y = mx + b.
    y= mx + b
    0 = -2/7(3) + b
    0 = -6/7 + b
    6/7 = b
    so the equation of the line perpendicular would be y = -2/7x + 6/7
  • Example 5
    Similar Problem: Write the slope-intercept form of the equation parallel to
    y= 8x + 3, which passes through (2, -5).
    y= 8x + 3 (the slope is 3 so the parallel slope is also 3)
    Use the parallel slope and the ordered pair to find the line of the equation.
    y= mx + b
    -5 = 3(2) + b
    -5 = 6 + b
    -11 = b
    y= 3x - 11 is the line parallel to the equation y = 3x + 8.
  • Example 6
    Similar Problem: Write the equation of a line parallel to the line y = 8, that passes through the point (2, 7).
    Hint: If a line is equal to y and have no x-value then the line parallel is the y-value of the ordered pair.
    So in this case it is y = 7.
  • Example 7
    Similar Problem: Write the equation of a line perpendicular to the line y = 8, that passes through the point (2, 7).
    Hint: If a line is equal to y and have no x-value then the line perpendicular is the is the x-value of the ordered pair.
    So in this case it is x = 2.