The differential equation dy/dx=(y-2)/(y+1)

Question

produces a slope field with horizontal tangents at y = 2
produces a slope field with vertical tangents at y = −1
produces a slope field with columns of parallel segments

a) I only <------- My answer ( This is correct??)
b) II only
c) I y II only
d) III only

Answer 1

I am between answer A and C???

Answer 2

Can you help me please????

Answer 3

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Since dy/dx = (y-2)/(y+1)
you are correct that I is correct.
But, II must also be correct, since you are trying to divide by zero

Since dy/dx is independent of x, it must produce rows of parallel segments.
But surely not columns, since y varies as you move vertically.

So, C is the answer.

Answer 4

Thank you