What is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ?

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What is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ?

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    2021-09-08T22:00:29+00:00

    Hello from MrBillDoesMath!

    Answer: y – (-8) =  (-14/11) (x -7)      or    y + 8 = (-14/11) (x-7)

    Steps:

    Let’s call  point  (7, -8)  (x1,y1) and point (-4,6)  (x2,y2). The point slope equation of a line through (x1, y1) is  

    y- y1 = m(x-x1)

    where “m” is the slope of the non-vertical line. Recall that m is rise/run or

    m  = (y2- y1)/(x2-x1).

    In our case

    m = (6 – (-8))/( -4 – 7)  =  (6 + 8)/ (-11)    = – 14/11

    The point-slope equation becomes

    y – (-8) =  (-14/11) (x -7)

    This can be rewritten as y + 8 = (-14/11) (x-7)

    As a final check,  you should verify that this equation passes through the original points using substitution!

    Regards, MrB.

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