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  1. krisshP's Avatar
    1 03-07-2012  13:24
    • Peer Of The TSR Realm
    • Posts: 1,655
    Lines
    Below are two lines:

    y=\frac{1}{3}

    y=-3

    Are these two lines parallel, perpendicular or neither?

    I'm stuck on this question. Aren't both lines parallel??:confused: This is because there is no gradient for both lines.
  2. blueray's Avatar
    2 03-07-2012  13:26
    • TSR Legend
    • Location: United States of Nippon
    Re: Lines
    1/3 times - 3 = -1

    therefore it is?? ( I know what it is, I am giving hint to op)
  3. krisshP's Avatar
    3 03-07-2012  13:30
    • Peer Of The TSR Realm
    • Posts: 1,655
    Re: Lines
    perpendicular in your viewpoint. However an x is NOT stated in both lines:confused:

    btw, I did do your method as well before. The answers page in my book says neither as the answer.:confused:
  4. claret_n_blue's Avatar
    4 03-07-2012  13:34
    • Exalted and Worshipped Member
    • Location: South East London
    • Posts: 1,337
    Re: Lines
    (Original post by krisshP)
    Below are two lines:

    y=\frac{1}{3}

    y=-3

    Are these two lines parallel, perpendicular or neither?

    I'm stuck on this question. Aren't both lines parallel??:confused: This is because there is no gradient for both lines.

    Let's say we have a line in the form:

    y = m + c

    where 'm' is the gradient and 'c' is the y-intercept.

    Then two lines are parallel if they have the same gradient
    Two lines are perpendicular if m = m'. By this I mean the gradient of one line is the negative reciprocal of the gradient in one of the other lines, m' = -\frac{1}{m}

    You have two ways of solving this:

    1) Write your two lines in the form y = mx + c and then go forwards from here, using the definitions I have given you.
    2) Plot both lines and see it geometrically, although most questions will require you do it algebraically. I'd recommend solving it algebraically and then checking it geometrically.
    Last edited by claret_n_blue; 03-07-2012 at 13:39.
  5. KyraBloke's Avatar
    5 03-07-2012  13:35
    • Exalted Member
    • Posts: 361
    Re: Lines
    y = 1/3 simply means the y value is always 1/3. If i was you i'd sketch the graph. It's a bit of a trick question in my opinion.

    No idea why i got a neg for this. Others are just over complicating things massively.
    Last edited by KyraBloke; 03-07-2012 at 13:49.
    Post rating:
    2
  6. krisshP's Avatar
    6 03-07-2012  13:39
    • Peer Of The TSR Realm
    • Posts: 1,655
    Re: Lines
    (Original post by claret_n_blue)
    Let's say we have a line in the form:

    y = m + c

    where 'm' is the gradient and 'c' is the y-intercept.

    Then two lines are parallel if they have the same gradient
    Two lines are perpendicular if m = m'. By this I mean the gradient of one line is the negative reciprocal of the gradient in one of the other lines, m' = -\frac{1}{m}

    First write your two lines in the form y = mx + c and then go forwards from here, using the definitions I have given you.
    But there is no x in both lines. This confuses me.
  7. krisshP's Avatar
    7 03-07-2012  13:42
    • Peer Of The TSR Realm
    • Posts: 1,655
    Re: Lines
    If there is no x in both lines, how is there a gradient in both lines?
  8. F1Addict's Avatar
    8 03-07-2012  13:46
    • Peer Of The TSR Realm
    • Posts: 1,733
    Re: Lines
    They're parallel. Dunno why everyone else is complicating things..
  9. notnek's Avatar
    9 03-07-2012  13:47
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: Lines
    (Original post by krisshP)
    If there is no x in both lines, how is there a gradient in both lines?
    You can rewrite the equations:

    \displaystyle y=0x + \frac{1}{3}

    \displaystyle y=0x - 3

    Does it make more sense now?
    Post rating:
    1
  10. krisshP's Avatar
    10 03-07-2012  13:50
    • Peer Of The TSR Realm
    • Posts: 1,655
    Re: Lines
    (Original post by notnek)
    You can rewrite the equations:

    \displaystyle y=0x + \frac{1}{3}

    \displaystyle y=0x - 3

    Does it make more sense now?
    Yes, it does make more sense now.

    Therefore both lines are parallel. However my says the answer is neither. Is this an error in the book??
  11. J10's Avatar
    11 03-07-2012  13:51
    • Exalted Member
    Re: Lines
    You could just draw the lines if you're ever in doubt
  12. notnek's Avatar
    12 03-07-2012  13:52
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: Lines
    (Original post by krisshP)
    Yes, it does make more sense now.

    Therefore both lines are parallel. However my says the answer is neither. Is this an error in the book??
    There is a mistake if the answer says they are not parallel.

    Try drawing them - they're clearly parallel.
  13. ztibor's Avatar
    13 03-07-2012  13:52
    • Peer Of The TSR Realm
    • Location: Hungary
    • Posts: 1,534
    Re: Lines
    (Original post by krisshP)
    Below are two lines:

    y=\frac{1}{3}

    y=-3

    Are these two lines parallel, perpendicular or neither?

    I'm stuck on this question. Aren't both lines parallel??:confused: This is because there is no gradient for both lines.
    There _is_ gradient but it is zero for both line (y=0*x-3 or y=0*x+1/3)
    that is these lines are parallel

    Generally arranging the equation ((x0,y0) a point on the line)
    \frac{y-y_0}{x-x_0}=m
    a) y=y_0 m=0, the line parallel with the axis x \alpha = 0


    b) x=x_0 \rightarrow m=tan \alpha=\infty \rightarrow \alpha=\frac{\pi}{2}
    the line perpendicular to the axis x
  14. krisshP's Avatar
    14 03-07-2012  13:54
    • Peer Of The TSR Realm
    • Posts: 1,655
    Re: Lines
    (Original post by notnek)
    There is a mistake if the answer says they are not parallel.

    Try drawing them - they're clearly parallel.
    I just drew both now using some online line creator. Both lines are parallel.

    Thanks a lot for your help.
  15. notnek's Avatar
    15 03-07-2012  13:57
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: Lines
    (Original post by krisshP)
    I just drew both now using some online line creator. Both lines are parallel.

    Thanks a lot for your help.
    No problem.

    You should try to learn how to draw x=a and y=b lines without using software. x=a lines are vertical lines that go through (a,0). y=b lines are horizontal lines that go through (0,b).
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