SOLUTION: I am studying for a final tomorrow, and I am really stuck on questions such as these: The lines 2x - 3y = -15 and 3x + ky = 12 are perpendicular. What is the value of k?

Question 315196: I am studying for a final tomorrow, and I am really stuck on questions such as these: The lines 2x - 3y = -15 and 3x + ky = 12 are perpendicular. What is the value of k?
Found 2 solutions by Fombitz, nerdybill:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Find the slope of each line.
Put each line in slope-intercept form, .
Perpendicular lines have slopes that are negative reciprocals.

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Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Since the two lines are perpendicular, their slopes are "negative reciprocals".
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Begin by putting both equation into the "slope-intercept" form:
2x - 3y = -15
-3y = -2x-15
y = (2/3)x+5
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3x + ky = 1
ky = -3x+1
y = (-3/k)x + 1/k
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Because the slopes are "negative reciprocal" we have the relation:
(2/3)(-3/k) = -1
(2/3)(3/k) = 1
(2)(k) = 1
2k = 1
k = 1/2
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