SOLUTION: For what value(s) of k the lines y=(k+1)x-3 and (2k-1)x+1 are parallel and are perpendicular?

Question 147073: For what value(s) of k the lines y=(k+1)x-3 and (2k-1)x+1 are parallel and are perpendicular?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For what value(s) of k the lines y=(k+1)x-3 and (2k-1)x+1 are parallel
:
Recognizing this in the form y = mx + b
You are given 2 slopes: m1 = (k+x) and m2 = (2k-1)
:
Parallel lines have equal slopes, therefore we can find k like this:
(2k-1) = (k+1)
2k - k = 1 + 1
k = 2
:
Substitute 2 for k in both equation and you can see they have equal slopes
y = 3x - 3 and y = 3x + 1
:
:
and are perpendicular?
The slope relationships of perpendicular lines are m1 * m2 = -1
:
(k+1) * (2k-1) = -1
FOIL
2k^2 + k - 1 = -1
2k^2 + k - 1 + 1 = 0
2k^2 + k = 0
Factor out k
k(2k+1) = 0
Two solutions
k = 0
and
2k = -1
k = -.5
Find the two equations when k = 0
y = 1x - 3 and y = -1x + 1 are perpendicular
and
when k = -.5
The two equations: y = .5x - 3, and y = -2x + 1 also are perpendicular
:
:
Did this make sense to you, any questions??
RELATED QUESTIONS
Find the value of k for which the lines (k + 1)x � 4y + 10 = 0 and y = (5/k)x + 11 are... (answered by josgarithmetic)

Determine k so that the lines r and s are parallel. r:(x-2)/3 = y/(-2) s:(x+5)/(-6) = (answered by josgarithmetic)

Find the value(s) of k such that the quadratic (k+1)x^2+2kx+2k=3(kx-1) has roots whose... (answered by thesvw)

Find the value of k if the lines 2x-3y=5 and 6x-(k+1)y =1 are... (answered by josgarithmetic)

4x+y=3 and (2k-1)x +(k-1)y=2k+1 is inconsistent ,find... (answered by KMST)

Two lines have slopes 2k-4 and k+6. What value(s) of k will produce perpendicular lines? (answered by jim_thompson5910)

Two lines have slopes 2k-4 and k+6. What value(s) of k will produce perpendicular lines? (answered by josmiceli)

If the lines 4x-y+2=0 and x+2ky+1=0 are perpendicular to each other, determine the value... (answered by tommyt3rd)

The line x+(2k-1)y = 6 and 3x+ky=2 are parallel.Fink... (answered by josgarithmetic)