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
Algebra.Com
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) (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 = x +
and
2x + (k+3)y = 4
(k+3)y = -2x + 4
y = x +
the slope of parallel lines are equal; therefore\
=
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
* = -1
= -1
= -1
2k = -1(5k+15)
2k = -5k - 15
2k + 5k = -15
7k = -15
k = value for perpendicular lines
RELATED QUESTIONS
find the value of k that will make the lines 2x + y = 3 and kx + y = -1 parallel (answered by tutor_paul)
If the lines 4x-y+2=0 and x+2ky+1=0 are perpendicular to each other, determine the value... (answered by tommyt3rd)
Find in each case the value of k so that the line r: y = kx + 1 is:
A) Parallel to the... (answered by Theo)
find the value of k so that the two given lines will be parallel: (k+2)x-5y=8 and... (answered by robertb)
For what value(s) of k the lines y=(k+1)x-3 and (2k-1)x+1 are parallel and are... (answered by ankor@dixie-net.com)
The vectors are shown as the x and y on top of each other but since I can’t type it out... (answered by ikleyn)
Find the value of k so that the lines 2x – 3y = 9 and kx-9y =18 will be... (answered by stanbon)
for what value of k will the line kx+5y=2k have slope equal to... (answered by josgarithmetic)
Two lines have slopes 2k-4 and k+6. What value(s) of k will produce perpendicular lines? (answered by jim_thompson5910)