Differential Equation

Question

The differential equation dy/dx = x/x-4.
I. will have a slope field with negative slopes in quadrant I
II. will have a slope field with positive slopes in all quadrants
III. will produce a slope field with columns of parallel tangents

I only

II only

III only

None of these

Answer 1

Plug in values as if you were graphing a function using a table.

x        dy/dx

 

-1       1/5

0          0

1         -1/3

2          -1

3          -3

4          undefined

5            5

6            3

 

There is only on vertical asymptote. The function has a maximum at x=0.

There's a horizontal aymptote.

But none of your choices fit this table...so the answer is none of these.