Question

@amistre64 calc!

Answer 1

last one i promise!! i just got confused on these problems and you actually explain it very well(:

Answer 2

the notations are bad in the options ...

dy/dx is something im used to seeing, not d/x

Answer 3

ohh thats ok(: maybe @Loser66 or @phi could help?

Answer 4

yeah they have typoes on left hand side but right hand side expressions look okay

Answer 5

oh! sorry i didnt look at it i thought you meant the right hand side, you can just ignore that, it is def a typo

Answer 6

it looks to me that when we try to use some points of reference that:

(x,y) = (x,-y)

Answer 7

so the slope doesn't depend on the "sign" of y
that means we must have \(y^2\) term on the right hand side for sure

Answer 8

or written another way:

x/y = x/-y

-xy = xy

hmm, x/y^2 seems to fit for me, but thats just with trial and error inputing a few of the more obvious points of reference

Answer 9

x^2/y^2 is always a positive number/slope soo that would leave us with x/y^2

Answer 10

so that would cancel out B and D!

Answer 11

A looks like a good option for me too @rational and @Loser66 agree too? (:

Answer 12

y^2 seems to be required, leaving us with A or D

x^2 is just not reasonable, leaving us with A

Answer 13

the slope field is drawn using what the slope of a line passing thru x,y would look like

in otherwords, dy/dx is defined to be a function of x and y for any given x,y coordinant

Answer 14

on the left side where x is negative, the top and bottom parts have negative slopes which tells us that y^2 is reasonable

since x^2/y^2 is at best always positive, and we have negative slopes .... then x/y^2 fits the bill

Answer 15

yes, x/y^2 seems to work
notice as y gets large x/y^2 becomes small (i.e. closer to 0 ) and the slope is flat.
similarly when |y| < 1, we get x/small # = large slope i.e. steep slope , with the sign of x
this matches the graph and clearly rules out x^2

Answer 16

thank you guys!