# 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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