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Homework Help: The equation of a straight line problems

  1. Dec 2, 2006 #1
    1. The problem statement, all variables and given/known data
    Find the equations of two lines through A. one parallel and the other perpendicular to the line defined by the given equation.
    [tex]A(-1,1),y=1[/tex]


    2. Relevant equations
    Parallel lines
    [tex]y = mx + b[/tex]
    then solve for b
    Perpendicular
    [tex]y = -mx + b[tex]
    then solve for b

    3. The attempt at a solution

    Parallel:
    [tex]y=1[/tex]
    [tex]y = 0 + b[/tex]
    [tex]1 = 0 + b[/tex]
    [tex]b = 1[tex]
    thus,
    [tex]y=1[/tex]


    Perpendicular:
    I got stuck at the perpendicular part.... because the answer from the back of my book is x = -1

    My answer is y = 1 also
     
  2. jcsd
  3. Dec 2, 2006 #2
    To get a perpendicular line, you need to swap the slopes (m) for their negative recipricol.

    Example:

    [tex]y=2x+5[/tex]

    is perpendicular to [tex]y=-\frac{1}{2}x+5[/tex]

    parallel you just change the b.

    I don't know if this helps, I hope it does.
     
  4. Dec 2, 2006 #3

    HallsofIvy

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    Science Advisor

    ?? do you mean you get y= 1 for a parallel and a perpendicular? Surely that can't be possible!


    You write:
    That's incorrect. A line perependicular to y= mx+ b has slope -1/m, not -m. Since for y= 1, m= 0, -1/m does NOT exist. What does that tell you?

    Rather than trying to plug numbers in to formulas, think! What does the line y= 1 look like? What would a line perpendicular to it look like?
     
  5. Dec 2, 2006 #4
    y = 1 is a horizontal line with slope 0. the perpendicular line will be vertical. what does that tell you about the slope?
     
  6. Dec 2, 2006 #5
    the slope will be -1?

    but x is 0 in y = 0x + 1? could it be that the slope cant be change?
     
  7. Dec 2, 2006 #6
    the slope of a vertical line is undefined.
     
  8. Dec 2, 2006 #7

    HallsofIvy

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    Science Advisor

    No, x is NOT 0 in "y= 0x+ 1"! The COEFFICIENT of x is 0. x can be any value.

    As Courtigrad pointed out, a vertical line does not have a slope. That was my point before. In fact, my other point was that you shouldn't be worrying about 'slope' at all! y= 1 is a horizontal line. Any line parallel to it must also be a horizontal line, of the form y= constant. Of course, that means it has slope 0 but that is not really important and confuses the issue with "perpendicular" lines. Vertical lines cannot be written in the form y= mx+ b! Obviously any line perpendicular to a horizontal line is vertical. What does the equation of any vertical line look like? What must the equation of a vertical line through (-1, 1) be?
     
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