Question 156304: Given two lines whose equations are 3x+y-8 =0 and -2x+by+9 =0, determine the value of b such that the two lines will be perpendicular.
Please help!!!!!!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 3x+y-8 =0 and -2x+by+9 =0
.
Start by determining the slope of
3x+y-8 =0
Do this by manipulating it into the "slope-intercept" form:
y = mx + b
where
m is the slope
b is the y-intercept at (0,b)
.
3x+y-8 =0
y-8 = -3x
y = -3x + 8
So, the slope is -3
.
Next, manipulate the other equation into the same form:
-2x+by+9 =0
by+9 =2x
by = 2x - 9
y = (2/b)x -9/b
.
For two lines to be perpendicular, the slopes must be negative reciprocal.
slope of first equation: -3
slope of second equation: 2/b
.
-3(2/b) = -1
3(2/b) = 1
3(2) = b
6 = b
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