Question

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

Answer 1

The correct option is (b)

Only II applies.

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.