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geometry

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If the slope of a line is 5/3 and a point on the line is (57,12) using the given point and the slope find the coordinates of the lattice point on the line?

  • geometry -

    The "point-slope" form of the equation of a straight line is:


    y - y1 = m ( x - x1 )


    (x1, y1) is a known point

    m is the slope of the line

    (x, y) is any other point on the line


    In this case:

    m = 5 / 3 , x1 = 57 , y1 = 12


    y - 12 = ( 5 / 3 ) (x - 57 )

    y = (5 x / 3 ) - ( 5 * 57 / 3 ) + 12

    y = (5 x / 3 ) - ( 285 / 3 ) + 12

    y = (5 x / 3 ) - 95 + 12

    y = (5 x / 3 ) - 83

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