The differential equation dy dx equals the quotient of the quantity x minus 3 and x plus 4

Question

1. produces a slope field with horizontal tangents at x = -4
2. produces a slope field with vertical tangents at x = -4
3. produces a slope field with columns of parallel segments

	I only
	II only
	I and II
	II and III only

Answer 1

dy/dx=(x-3)/(x+4)

To have a horizontal tangent, the slope or dy/dx must be zero. That happens when x=3

To have a vertical tangent, the slope or dy/dx must be infinity. That happens when x=-4

To have columns of parallel segments dy/dx must be the same value irrespective of the value of x.

That is not the case here.

So, the answer is II only.