The differential equation dy dx equals the quotient of the quantity x minus 2 and y minus 2.

I) produces a slope field with horizontal tangents at y = 2

II) produces a slope field with vertical tangents at y = 2

III) produces a slope field with columns of parallel segments

a) I only

b) II only

c) I and II

d) III only

The correct option is (b)

Only II applies.

Step-by-step explanation:

Given

dy/dx = (x - 2)/(y - 2)

We want to check which of the given options is true.

I) produces a slope field with horizontal tangents at y = 2

This is not true

II) produces a slope field with vertical tangents at y = 2

This is true because putting y - 2 = 0, we have dy/dx ---> infinity.

Which is a slope field with vertical tangents at y - 2 = 0 or y = 2.

III) produces a slope field with columns of parallel segments

This is not true.

i think that you should ask google for the answer to that problem because if we don't know it google does

the answer will be b x² +x-1

step-by-step explanation: