# Slope Field for Differential Equation

• Jan 24th 2010, 07:34 AM
rawkstar
Slope Field for Differential Equation
The slope field for the differential equation dy/dx=(3y)/(xy+5x) will have vertical segments when

A) x=0, only
B) y=0, only
C) y=-5, only
D) y=5, only
E) x=0 or y=-5

Im not sure what this question is asking for, we have never used the term slope field in class. I do know that something with a vertical slope has a derivative of undefined though. Please help
• Jan 24th 2010, 07:48 AM
rawkstar
I think I answered my question. The slope field has vertical segments whenever the derivative is undefined. So I did trial in error with all my answer options and found that whenever x=0 or y=-5, the denominator of dy/dx=0 thus making it undefined, thus giving the slope field vertical segments.
• Jan 24th 2010, 08:27 AM
skeeter
Quote:

Originally Posted by rawkstar
I think I answered my question. The slope field has vertical segments whenever the derivative is undefined. So I did trial in error with all my answer options and found that whenever x=0 or y=-5, the denominator of dy/dx=0 thus making it undefined, thus giving the slope field vertical segments.

trial and error? what if the answer choices were not available?

\$\displaystyle xy+5x = 0\$

\$\displaystyle x(y+5) = 0\$

\$\displaystyle x = 0\$ , \$\displaystyle y = -5\$