1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    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

    User Avatar
    Staff Emeritus
    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The equation of a straight line problems
  1. Straight line problem (Replies: 7)

Loading...