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Math Help - graph of a point that passes through a line

  1. #1
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    graph of a point that passes through a line

    no clue what to do, help please

    write an equation for a line tha tasses through (5,4) and is perpinducular to the graph of 2x - 3y = 1



    thank you!!!1
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  2. #2
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    Quote Originally Posted by Ilovemath123 View Post
    no clue what to do, help please

    write an equation for a line tha tasses through (5,4) and is perpinducular to the graph of 2x - 3y = 1



    thank you!!!1
    You need to find two things: the gradient of the line and a point on the line.

    Get those two things and substitute into the general equation

    y - y_1 = m(x - x_1)

    where m is the gradient and \, (x_1, \, y_1)\, is a point on the line.

    The point on the line is given on a platter. It's (5, 4).

    As for the gradient, you know that it's perpendicular to the line 2x - 3y = 1 \Rightarrow 2x - 1 = 3y \Rightarrow y = \frac{2}{3} x - \frac{1}{3}.

    Therefore: m \times \frac{2}{3} = -1 \Rightarrow m = .....

    (You do know that when two lines are perpendicular, the product of their gradients is equal to -1, right?)
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  3. #3
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    Quote Originally Posted by Ilovemath123 View Post
    no clue what to do, help please

    write an equation for a line tha tasses through (5,4) and is perpinducular to the graph of 2x - 3y = 1



    thank you!!!1
    Two lines are perpendicular to another if their slopes are the negative reciprocals of each other.

    y=mx+b where m is the slope, b is y-intercept.
    y=(2/3)x-(1/3)
    m=2/3

    the line you want has slope -(3/2).
    y=-(3/2)x+b

    plug in (5,4) to solve for b.

    4=-(3/2)5+b
    b=11.5

    your line is y=-(3/2)x+11.5
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  4. #4
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    Quote Originally Posted by Ilovemath123 View Post
    write an equation for a line tha tasses through (5,4) and is perpinducular to the graph of 2x - 3y = 1
    Unfortunately I have no chance against all those fast-typers...

    So you get a drawing
    Attached Thumbnails Attached Thumbnails graph of a point that passes through a line-gereaden_orthogon.jpg  
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