Answer:
line b and c are perpendicular because the product of their slope is -1
Step-by-step explanation:
For two lines to be parallel they must have the same slope
For two line to be perpendicular, the product of their slope must be -1
Line a: 2x-7y=14
Rewrite in the form y = mx+c
-7y = -2x + 14
y = -2/-7 x + 14/-2
y = 2/7x - 7
The slope of line a is 2/7
Line b: y=7/2x-8
This is already in standard format
mx = 7/2 x
m = 7/2
The slope of line b is 7/2
Line c: 2x+7y=21
Rewrite in standard form
7y = -2x + 21
y = -2/7 x + 21/7
y = -2/7 x + 3
The slope of line c is -2/7
Take the product of line b and c
mb * mc = 7/2 * -2/7
mb * mc = -1
Hence line b and c are perpendicular because the product of their slope is -1
