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Math Help - straight line

  1. #1
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    straight line

    a straight line equation y=4x-5

    i found the xy intercept

    (5/4, -5)

    question (a) find a line that is perpendicular and passes the point (1,2)
    quesiton (b) at what coordinates do the lines cross.

    is there a way to find by calculation? or do i just draw the lines?


    many thanks
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  2. #2
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    For a perpendicular line, you need m_1*m_2=-1

    m_1 represents the gradient of the original equation and m_2 represents the gradient of the perpendicular line.

    4*m_2=-1
    m_2=-\frac{1}{4}

    Therefore the gradient of your perpendicular line is -\frac{1}{4}

    y=mx+c
    y=-\frac{1}{4}x+c

    Sub in the point they give you (1,2) and solve for c.

    2=-\frac{1}{4}(1)+c

    Can you continue from here?

    To find the intersection of the two graphs, let the two equations equal each other.
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  3. #3
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    Quote Originally Posted by decoy808 View Post
    a straight line equation y=4x-5

    i found the xy intercept

    (5/4, -5)
    What do you mean by "xy intercept"? The "x-intercept" is the point where the line crosses the x-axis; where y= 0 so x= 5/4 and the point is (5/4, 0). The "y-intercept is the point where the line crosses the y-axis: where x= 0 so y= -5 and the point is (0, -5). But I have never heard of an "xy intercept" and the point (5/4, 5) is not on this line.

    question (a) find a line that is perpendicular and passes the point (1,2)
    Use the fact that if y= mx+ b and y= nx+ b are perpendicular then mn= -1.
    Your first line has slope 4 so you are looking for the equation of the line through (1, 2) with slope -1/4

    quesiton (b) at what coordinates do the lines cross.

    is there a way to find by calculation? or do i just draw the lines?


    many thanks
    Solve the two equations simultaneously. If you have them in the form y= mx+ a and y= nx+ b, the first step is easy: subtract one of the equations from the other and the "y" cancels leaving one equation for x.
    Last edited by mr fantastic; November 30th 2009 at 02:59 AM. Reason: Added quote tag.
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  4. #4
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    okey i got

    x= 11/17
    y= 41/17

    is this correct?
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by decoy808 View Post
    okey i got

    x= 11/17
    y= 41/17

    is this correct?
    [1] \boxed{y = 4x-5}

    Now, determine the equation of the line perpendicular to [1] through (1, 2) having a slope of -1/4.


    y=mx+b where y = 2, x = 1, m= -1/4

    2=-\frac{1}{4}(1)+b

    8=-1+4b

    9=4b

    b=\frac{9}{4}

    [2] \boxed{y=-\frac{1}{4}x+\frac{9}{4}}

    Solve the system [1] and [2].

    Your solution is incorrect. Check it again.
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