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algebra

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Is this pair of lines parallel, perpendicular, or neither?

2x+5y=7
5x-2y=8

  • algebra -

    the slope of the first is -2/5 and the slope of the second is 5/2

    notice their product is -1, so they are perpendicular.
    (slopes are negative reciprocals of each other)

    (to get the slope in my head I used the rule:
    for Ax + By = C, slope = -A/B )

  • algebra -

    Change into the standard equation for a straight line of y = mx + b
    2x+5y=7 and
    5y = -2x+7 then divide by 5 to obtain
    y=(-2/5)x + 7/5

    Second equation is
    5x-2y=8
    -2y=-5x+8
    multiply by -1
    2y=5x-8
    y=(5/2)x-4

    Lines are parallel if the slopes are equal. Lines are perpendicular if the slopes are the negative reciprocal of each other.
    -

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