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Question 216996: Find k that so that the line through (4,4) and (k,8) is
a) parallel to 3y-4x=7
b) perpendicular to 4y+5x=1
Answer by chibisan(131)   (Show Source):
You can put this solution on YOUR website! a )
parallel = same grad
3y= 7+4x
make y the subject
y= 7/3 + 4/3x
grad = 4/3
grad of line through (4,4) and (k,8) . leave k as it is
grad = 4-8 / 4-k
4/3 = -4 / 4-k
cross multiply it ,
16-4k=-12
16+12 = 4k
k = 7 (ans)
b)
perpendicular = negative reciprocal
4y+5x=1
make y the subject always.
4y=1-5x
y= 1/4 - 5/4x
grad= -5/4
perpendicular grad = 4/5
from previous steps , -4/4-k is the grad so ,
4/5 = -4/4-k
cross multiply ,
16 - 4k = -20
16+20 = 4k
k = 9 (ans)
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