algebra
posted by C on .
Is this pair of lines parallel, perpendicular, or neither?
2x+5y=7
5x2y=8

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 ) 
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
5x2y=8
2y=5x+8
multiply by 1
2y=5x8
y=(5/2)x4
Lines are parallel if the slopes are equal. Lines are perpendicular if the slopes are the negative reciprocal of each other.
