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Math Help - Equations of A Straight Line. Please Help Me.

  1. #1
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    Equations of A Straight Line. Please Help Me.

    Can someone please help me:

    1) Find the equation of a straight line that passes through the point (2,3) and is parallel to the line with equation 3x + 4y -8 = 0.

    2) Find the equation of a line that passes through (-2,4) and is perpendicular to the line 4x + 3y = 6.

    Pleassseee Help.
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  2. #2
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    1) Find the equation of a straight line that passes through the point (2,3) and is parallel to the line with equation 3x + 4y -8 = 0.
    When the equation of a line is
    ax+by +c = 0


    where a,b and c can be positive or negative

    its slope is given by (-b)/a

    -for being parralel slopes should be same

    -for two lines being perpendicular the slopes will multiply to give -1

    it can also be represented as

    y= -bx/a +c

    any point(m,n) lying on this should satisfy the equation

    which means whenever you will put

    am+bn+c

    the value you will get is "0"



    1)

    Let the line be given by

    y = mx+c

    Since it is parallel to
    3x+4y-8 =0

    its slope will be same

    Thus the value of "m" is -4/3

    y= (-4x/3) + c

    Put the value of (x,y) as (2,3)

    Thus

    3 = -8/3 + c
    Thus c= 17/3

    y=-4x/3 + 17/3

    2)

    y= mx +c

    since it is perpendicular to
    4x + 3y = 6.


    Thus
    m * -3/4 = -1
    Hence

    m= 4/3

    Thus
    y= (4x/3) +c

    4 = -8/3 +c

    c= 20/3

    y= 4x/3 +20/3
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