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17 April, 06:16

If two lines, written in standard form, are a1x + b1y = c1 and a2x = b2y = c2, what is the relationship of a1, a2, b1, and b2 if the lines are parallel?

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  1. 17 April, 06:34
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    hello:

    a1x + b1y = c1 ... (1)

    a2x = b2y = c2, ... (2)

    the lines are parallel when has same slope

    calculate the slope of the line (1):

    a1x + b1y = c1

    b1y = c1 - a1x

    if : b1 ≠ 0 : y = (-a1/b1) x + c1/b1

    the slope is : - a1/b1

    same method the slope of the line (2) is : - a2/b2

    the relationship of a1, a2, b1, and b2 if the lines are parallel is:

    -a1/b1 = - a2/b2
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