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line l and and line k are perpendicular. line l has a slope of 3. line k contains the points (5,8) and (2, y). what is the value of y?

  • Algebra -

    line l has slope 3, so line k haas slope -1/3

    using the point-slope form of a line,

    (y-8) = -1/3 (x-5)
    3y-24 = 5-x
    3y = 29-x

    so, if (2,y) is on the line,

    3y = 29-2 = 27
    y = 9

    Or, without quite so much algebra, knowing that line k has slope 1/-3, we know that y increases by 1 when x decreases by 3.

    going from (5,8) to (2,y), x has decreased by 3, so y increases by 1, from 8 to 9.

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