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March 24, 2017

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Find equation of the line that passes through the points (2/3,-5/4) and (-3,-5/6). write your answer in slope-intercept form and standard form with integer coefficients.

  • math - ,

    The slope m of a line passing through two points (x1, y1), (x2, y2) is given by

    m = (y2-y1)/(x2-x1)
    m = (-5/6 - -5/4) / (-3-2/3) = (5/12) / (-11/3) = -15/132 = -5/44

    The equation for a straight line is of the form y = m*x + b

    where m is the slope and b is the y-intercept.

    So far we have;

    y = -5/44*x + b

    To solve for b, plug in one of the points:

    -5/4 = -5/44 * (2/3) + b
    -5/4 = -10/132 + b

    b = -5/4 + 10/132 = -155/132

    y = -5/44*x - 155/132 (slope-intercept form)

    Standard form: You need to find the common factors of 44 and 132: it's 132, so multiply the equation by 132:

    132*y = -15*x - 155
    -15*x + 132*y = -155

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