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Math Help - Graphing an equation

  1. #1
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    Graphing an equation

    The graph of which of the following lines contains the point (5,0) and makes an angle of 45 degrees with the positive x-axis?

    Now the solution is y=x-5 but why couldn't the solution be y=(3x-15)/2 or y=2x+10?? I guess I'm stuck on the the 45 degree part..
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  2. #2
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    Quote Originally Posted by donnagirl View Post
    The graph of which of the following lines contains the point (5,0) and makes an angle of 45 degrees with the positive x-axis?

    Now the solution is y=x-5 but why couldn't the solution be y=(3x-15)/2 or y=2x+10?? I guess I'm stuck on the the 45 degree part..
    Formula: m = \tan \theta where \theta is the angle the line makes with the positive x-axis.
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  3. #3
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    Still am not sure...do you mean "m" is the slope?? And also why does it have to be tangent? Why not sin or cos?
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  4. #4
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    It is  tan \;\theta because it has been proven.

    We know from coordinate geometry that the gradient of a straight line is the rise over run.

    Consider the following triangle attached at the bottom of this post:
    (Note: the diagonal line is "straight line" whose equation you are looking for)

    If the gradient of the diagonal line is symbolised by the letter m

     m = \frac {rise}{run}

    = \frac {opposite}{adjacent}
    From trigonometry, we know that  \frac {opposite}{adjacent} is also  tan \;\theta

    Therefore  m = tan\;\theta

    To find the equation of a straight line, you need a point  (x_1,y_1) and gradient m.
    Attached Thumbnails Attached Thumbnails Graphing an equation-tan-theta.bmp  
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