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Math Help - Where does the plane intersect the axis?

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    Question Where does the plane intersect the axis?

    Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.
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    Re: Where does the plane intersect the axis?

    Quote Originally Posted by jessicadowning View Post
    Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.
    To find the x-intercept set the y and z coordinates equal to zero. This gives

    3x-4(0)+0=12 \iff x=4 \iff (4,0,0)

    Now do the same thing with y and z, set the other two coordinates to zero.

    To find the equation of the line in the xy plane, set z=0

    This gives

    3x-y=12 \iff y=3x-12

    Again do the same thing with the other two coordinates.
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