Question

The differential equation dy dx equals the quotient of the quantity y minus 2 and y plus 1

produces a slope field with horizontal tangents at y = 2
produces a slope field with vertical tangents at y = −1
produces a slope field with columns of parallel segments

Answer 1

https://gyazo.com/40b80568af9602738d4d7c64db1bb2e1

Answer 2

@zepdrix

Answer 3

I was thinking C since the denominator would be bigger.

Answer 4

\[\large\rm y'(y)=\frac{y-2}{y+1}\]At y=2,\[\large\rm y'(2)=\frac{2-2}{2+1}\]Hmm, so what is this telling us?\[\large\rm y=2, \qquad\qquad y'=0\]

Answer 5

Oh I didn't look at the options yet hehe

Answer 6

Horizontal line

Answer 7

So first line is definitely true, cool.

Answer 8

10/10 IGN

Answer 9

Looks like the second one is true also, ya?
Bottom blows up, corresponding to "infinite" slope, asymptotic behavior.

Answer 10

I didn't even look at the third option yet :P
Just seems like we land on C by checking the first two automatically lol

Answer 11

Clearly III can't be true if I and II are true, right?
If we have vertical tangents,
and we also have horizontal tangents in other places,

then we don't have parallel tangent lines.

Answer 12

I was thinking about it in a completely different way.

Answer 13

Then I noticed it was asking about the slope fields.

Answer 14

In all three where as I misread I and II and eliminated them using some thought (yes I thought wrong ;p) thanks