SOLUTION: If the line ax+y=c is perpendicular to the line x-by=d, then b=?

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Question 678242: If the line ax+y=c is perpendicular to the line x-by=d, then b=?
Found 2 solutions by pmatei, MathLover1:
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
The slopes of perpendicular lines are opposite reciprocal of each other: m%5B1%5D=-%281%2Fm%5B2%5D%29
So you need to re-write your line equations in a form that gives you the slope. I will use slope-intercept form:
ax%2By=c becomes y=-ax%2Bc with m%5B1%5D+=+-a
x-by=d becomes y=%281%2Fb%29x-d%2Fb with m%5B2%5D+=+1%2Fb
Replacing m%5B1%5D and m%5B2%5D into the relation between slopes of perpendicular lines:
-a+=+-b
Thus
b=a

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
ax%2By=c
x-by=d
first write it in slope-intercept form
y=-ax%2Bc .......slope is m=-a
-by=-x%2Bd
y=%28%28-1%29%2F%28-b%29%29%28x%2Bd%29
y=%281%2Fb%29%28x%2Bd%29.......slope is m%5B1%5D=1%2Fb


if a line is perpendicular to the other line , then slopes are negative reciprocals: m=-%281%2Fm%5B1%5D%29
so, -a=-%281%2F%281%2Fb%29%29
-a=-%28b%2F1%29
-a=-b
and
b=a