SOLUTION: The line 3kx + 8y = 5 is perpendicular to the line 6y

SOLUTION: The line 3kx + 8y = 5 is perpendicular to the line 6y - 4kx = -1. Find k.

Question 1186115: The line 3kx + 8y = 5 is perpendicular to the line 6y - 4kx = -1. Find k.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The line is perpendicular to the line .
Find .
write both lines in slope intercept form:

=> a slope is

=> a slope is

recall that perpendicular lines have a slopes negative reciprocal to each other
so,
then

.......cross multiply

...simplify

=> or

then, your lines are:

or

or

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The response from the other tutor shows a good elementary method for solving the problem using the slopes of the lines, knowing that lines that are perpendicular have slopes that are negative reciprocals of each other. You should understand and be able to use that method for solving any problem like this.

For more advanced students, there is a much faster path to the solution:

The lines with equations Ax+By=M and Cx+Dy=N are perpendicular if and only if AC+BD=0.

For this problem, the equations are

(3k)x+(8)y=5
(-4k)x+(6)y=-1

For the lines to be perpendicular, then, the requirement is

or

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