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Geometry

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1. Why do you think that the slope of a vertical line is called "undefined?"

2. Can you find the equation of a line if you are given the slope and the x-intercept? If so, explain how. If not, explain why you can't.

  • Geometry -

    Consider any two points that form a vertical line,
    e.g. (x, a) and (x, b)

    slope = (b-a)/(x-x)
    = (b-a)/0 , but division by zero is "undefined"

    Thus the slope of a vertical line is undefined.

    2. Yes, given the slope m and the x-intercept we can find the equation of the line
    e.g. slope = 4 , x-intercept is (3,0)

    y = 4x + b
    but (3,0) lies on it, so
    0 = 4(3) + b
    b = -12
    y = 4x - 12

    in general if the slope is m and the x-intercept is k
    the equation is
    y = m(x-k)

    for the above, y = 4(x-3)
    which expands to y = 4x - 12 , as above.

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