INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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Text Comments (4)

3 answers

Last reply by: Dr Carleen Eaton
Sat Sep 14, 2013 2:39 PM

Post by leo leyva on July 16, 2013

i think at minute 14:20 in the equation on the step -8y=-3/-8(x)+2/-8 you simplified wrong the slope... you didnt turn it into a negative you left it as a positive. or am i wrong? sincerely confused)

Parallel Lines and Perpendicular Lines

  • Parallel lines are two lines in the same plane that do not intersect. Two non-vertical lines are parallel if and only if they have the same slope.

  • If you are given the equation of a line and a point not on that line, you can find the equation of the line through this point parallel to the given line by using the point-slope form.

  • Perpendicular lines are lines that intersect at right angles. Two non-vertical lines are perpendicular if and only if the product of their slopes is –1 (or, equivalently, their slopes are negative reciprocals of each other).

  • You can use this fact to determine whether a pairs of lines whose equations have been given are perpendicular or not.

  • If you are given the equation of a line and a point, you can find the equation of the line through this point perpendicular to the given line by using the point-slope form. You must first find the slope of the given line and then take its negative reciprocal.

Parallel Lines and Perpendicular Lines

A line is parallel to the line whose equation is
y = − [1/4]x − 3
This line also passes through the point ( - 5,7)
Find the equation of this line in slop intercept form.

  • y = mx + b
    parallel lines have the same slope
    m = − [1/4]b = ?
  • 7 = − [1/4]( − 5) + b
  • 7 = [5/4] + b
  • 7 = 1[1/4] + b
  • 5[3/4] = b

y = − [1/4]x + 5[3/4]

A line is parallel to the line whose equation is
y = − [3/7]x + 6
This line also passes through the point ( - 4,2)
Find the equation of this line in slop intercept form.

  • y = mx + b
    parallel lines have the same slope
    m = − [3/7]b = ?
  • 2 = − [3/7]( − 4) + b
  • 2 = [12/7] + b
  • 2 = 1[5/7] + b
  • [2/7] = b

y = - [3/7]x + [2/7]

Are the lines determined by the equations
3x − 6y = 18
4x − 2y = 12
parallel, perpendicular, or neither?

  • 3x − 6y = 18
  • − 6y = 18 − 3x
  • y = [(18 − 3x)/( − 6)]
  • y = [18/( − 6)] − [3x/( − 6)]
  • y = − 3 + [x/2]m = [1/2]
  • 4x − 2y = 12
  • − 2y = − 4x + 12
  • y = [( − 4x + 12)/( − 2)]
  • y = 2x − 6m = 2
  • ([1/2]) ≠ − 1
  • ([1/2]) ≠ (2)

neither

Are the lines determined by the equations
5x − 2y = 10
2x + 12y = 24
parallel, perpendicular, or neither?

  • 5x − 2y = 10
  • − 2y = − 5x + 10
  • y = [( − 5x)/( − 2)] + [10/( − 2)]
  • y = [5/2]x − 5m = [5/2]
  • 2x + 12y = 24
  • 12y = − 2x + 24
  • y = [( − 2x)/12] + [24/12]
  • y = − [x/6] + 2m = − [1/6]
  • (−[1/6])([5/2]) ≠ − 1
  • (−[1/6]) ≠ ([5/2])

neither

A line passes through the point ( - 4, - 3) and is perpendicular to the line whose equation is y = 1/5 x − 6. Find the equation of this line in slope intercept form.

  • y = mx + b
    m = [1/5]
    negative reciprocal = - 5
  • − 3 = − 5( − 4) + b
  • − 3 = 20 + b
  • − 23 = b

y = − 5x − 23

A line passes through the point (5,4) and is perpendicular to the line whose equation is y = − 7/10 x + 3. Find the equation of this line in slope intercept form.

  • y = mx + b
    m = − [7/10]
    negative reciprocal = [10/7]
  • 4 = [10/7](5) + b
  • 4 = [50/7] + b
  • 4 = 7[1/7] + b
  • - 3[1/7] = b

y = [10/7]x − 3[1/7]

A line is perpendicular to the line whose equation is 2x − 4y = 8. This line also passes through the y - intercept of the graph of x − 5y = 20. Find the equation of this line in slope intercept form.

  • 2x − 4y = 8
  • − 4y = − 2x + 8
  • y = [( − 2x + 8)/( − 4)]
  • y = [1/2]x − 2
  • m = [1/2]
    slope of perpendicular line = - 2
  • x − 5y = 20
  • − 5y = − x + 20
  • y = [( − x + 20)/( − 5)]
  • y = [1/5]x − 4b = − 4

y = − 2x + 4

A line is perpendicular to the line whose equation is 3x − 7y = 42. This line also passes through the y - intercept of the graph of 6x + 3y = 30. Find the equation of this line in slope intercept form.

  • 3x − 7y = 42
  • − 7y = − 3x + 42
  • y = [( − 3x + 42)/( − 7)]
  • y = [3/7]x − 6
    negative reciprocal = − [7/3]
  • 6x + 3y = 30
  • 3y = − 6x + 30
  • y = [( − 6x + 30)/3]
  • y = − 2x + 10
    b = 10

y = − [7/3]x + 10

A line is parallel to the line whose equation is
y = − [2/5]x − 6
This line also passes through the point ( - 10,12)
Find the equation of this line in slop intercept form.

  • y = mx + b
    parallel lines have the same slope
    m = − [2/5]b = ?
  • 12 = − [2/5]( − 10) + b
  • 12 = [20/5] + b
  • 12 = 4 + b
  • 16 = b

y = − [2/5]x + 16

A line passes through the point ( - 6, - 4) and is perpendicular to the line whose equation is y = − 2/3 x + 8. Find the equation of this line in slope intercept form.

  • m = − [2/3]
    negative reciprocal = [3/2]
  • − 4 = [3/2]( − 6) + b
  • − 4 = [( − 18)/2] + b
  • − 4 = − 9 + b
  • 5 = b

y = [3/2]x + 5

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Parallel Lines and Perpendicular Lines

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Mathematics: Algebra 1