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?

Algebra ->  Linear-equations -> 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?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of each line.
Put each line in slope-intercept form, y=mx%2Bb.
Perpendicular lines have slopes that are negative reciprocals.
m1%2Am2=-1
.
.
.
2x-3y=-15
-3y=-2x-15
y=%282%2F3%29x%2B5
m1=2%2F3
.
.
.
3x+%2B+ky+=+12
ky=-3x%2B12
y=-%283%2Fk%29x%2B12
m2=-%283%2Fk%29
.
.
.
m1%2Am2=-1
%282%2F3%29%28-%283%2Fk%29%29=-1
highlight%28k=2%29

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