SOLUTION: For what value(s) of k will the lines kx+5y=2 and 2x+(k+3)y=4 be: a) parallel to each other? b)perpendicular to each other

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Question 922400: For what value(s) of k will the lines
kx+5y=2 and 2x+(k+3)y=4 be:
a) parallel to each other? b)perpendicular to each other
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For what value(s) of k will the lines
kx+5y=2 and 2x+(k+3)y=4 be: a) parallel to each other?
:
put both equations in the slope intercept form
kx + 5y = 2
5y = -kx + 2
y = -k%2F5x + 2%2F5
and
2x + (k+3)y = 4
(k+3)y = -2x + 4
y = -2%2F%28%28k%2B3%29%29x + 4%2F%28%28k%2B3%29%29
the slope of parallel lines are equal; therefore\
-k%2F5 = -2%2F%28%28K%2B3%29%29
cross multiply
-k(k+3) = 5 * -2
-k(k+3) = -10
multiply both sides by -1
k(k+3) = 10
k^2 + 3k - 10 = 0
factors to
(k+5)(k-2) = 0
the positive solution
k = 2
the negative solution will also work
k = -5
:
:
b)perpendicular to each other
the relationship of slopes of perpendicular lines: m1 * m2 = -1, therefore
-k%2F5 * -2%2F%28%28k%2B3%29%29 = -1
%282k%29%2F%285%28k%2B3%29%29 = -1
%282k%29%2F%28%285k%2B15%29%29 = -1
2k = -1(5k+15)
2k = -5k - 15
2k + 5k = -15
7k = -15
k = -15%2F7 value for perpendicular lines