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Math Help - reflection in the line y = x+1???

  1. #1
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    reflection in the line y = x+1???

    If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.
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  2. #2
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    Quote Originally Posted by usagi_killer View Post
    If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.
    When you reflect a line over y = x, you simply switch the x and y variables.

    So y = 2x + 3 becomes

    x = 2y + 3

    2y = x - 3

    y = \frac{1}{2}x - \frac{3}{2}

    The resulting equation of a line is also known as the inverse of the original equation.

    In the problem, the line was reflected over y = x + 1, so you add 1 to the inverse of the original equation.

    y = \frac{1}{2}x - \frac{3}{2} + 1

    y = \frac{1}{2}x - \frac{1}{2}

    If you drew y = 2x+3 and y = \frac{1}{2}x - \frac{1}{2} on graph paper and folded the paper at y = x + 1, the two lines should be right on top of each other.
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