Question

(K+1)x+2y=6; M=k-2

Answer 1

Apparently you mean that M is the slope. Most folks use lower-case letters.

In any case, we have

2y = -(k+1)x + 6
y = -(k+1)/2 x + 3
The slope is -(k+1)/2

-(k+1)/2 = k-2
-(k+1) = 2k - 2
-k-1 = 2k-2
3k = 1
k = 1/3

Answer 2

oops
-(k+1) = 2k - 4
-k-1 = 2k-4
3k=3
k=1

Answer 3

Steve, You made another mistake in that second edit.

Once you reach -k-1=2k-4.

You need to subtract 2k from the right side.
That gets you -3k-1=-4.

You add 1 to get rid of that negative one which gets -3k=-3. Solve for k=1