Question

The differential equation dy/dx= (x+2)/(y-5)

I. Produces a slope field with vertical tangents at y=5
II. Produces a slope field with vertical tangents at x=-2
III. Produces a slope field with rows of parallel segments

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

Answer 1

A. I only

Explanation:

As
`(dy)/(dx) =(x+2)/(y-5)` yields an undefined value when y=5, I is true

At x=-2, the slope field will have a slope of 0, so II is false

III is false as the slope field shows otherwise.

(Desmos has a slope field feature that is very helpful)