Question

X - 7y = 10 and 2x +14y = 21 are they perpendicular, parallel, or neither

Answer 1

X - 7y = 10
-7y = -x + 10
y = 1/7x - 10/7....slope here is 1/7, y int = -10/7

2x + 4y = 21
4y = -2x + 21
y = -1/2x + 21/4...slope is -1/2, y int = 21/4

neither <==

for them to be parallel, they would need the same slope
for them to be perpendicular, they would need negative reciprocal slopes
they have neither

Answer 2

To decide, you would better find their slopes

x - 7y = 10
-7y = 10-x
y = 1/7 x -10/7

the slope = 1/7




2x +14y = 21
14y = 21 - 2x
y = 21/14 - 2/14 x
y = -1/7 x + 3/2

the slope = -1/7

For parallel lines:
"All parallel lines have the same slope!"

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For perpendicular lines:
"Their slopes' product is -1"

For our case, they are not parallel nor perpendicular