Find the value of k so that (k+1)x +2y=6 has a slope of m=k-2
we have the equaton
(k+1)x +2y=6
step 1
isolate the variable y
2y=-(k+1)x+6
Divide by 2 both sides
y=-[(k+1)/2]x+3
this is the equation of the line in slope intercept form
y=mx+b
where
the slope is
m=-(k+1)/2
equate the slope to (k-2)
-(k+1)/2=k-2
solve for k
-(k+1)=2k-4
-k-1=2k-4
2k+k=-1+4
3k=3
k=1