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

Question

I.produces a slope field with horizontal tangents at y = 2
II.produces a slope field with vertical tangents at y = -1
III.produces a slope field with columns of parallel segments

A. I only
B. II only
C. I and II
D. III only

Answer 1

I. yes
II. No - vertical segments at y=+1
III. No. For any x, the slopes change with y.
In fact, you will get rows of parallel segments, since for any y, the slope does not change with x.

you can graph slope fields at desmos.com

Answer 2

Thank you