Can someone show me how to graph xy = 15?

Question

e.mccormick · Answer

Find y, graph a few points, like the y intercept. and watch out for x=0.

e.mccormick · Answer

Oh, and finding the y intercept is actually a bit of a trick.... you may notice there is not one.  There is also not an x intercept.

e.mccormick · Answer

When you solve for y, you get:

$y=\frac{15}{x}$

Any x that evenly divides 15 is a good point to use.  So $x=\{-3,-1.5,1.5,3\}$ give useful points.

anonymous · Answer

Okay.

e.mccormick · Answer

Then play connect the dots.  Remember, you can't cross either the x or y axis.

e.mccormick · Answer

(1,15), (15,1), (-1,-15), (-15,-1)  are also there, so you have an idea what happens to the tails.

e.mccormick · Answer

The lack of an x or y intercept is one of the big clues to the shape.  Do you know what that means?  What quadrants your points are in is the other part of this clue.

anonymous · Answer

attachment

e.mccormick · Answer

Yep! https://www.desmos.com/calculator/n7xd8g8ojy

anonymous · Answer

Thanks!

anonymous · Answer

Could you help me with one more?

e.mccormick · Answer

Sure, but first... one concept from this type graph becomes super important later in math.  Can you guess why the graph shoots up and down as it gets close to the origin?

anonymous · Answer

Not exactly sure.

anonymous · Answer

Because it is undefined?

e.mccormick · Answer

$y=\frac{15}{x}$  Well, what if x is really small?  Close to 0.
Say $x=\frac{1}{100}$

$$y=\frac{15}{\frac{1}{100}}\
y=\frac{15}{1}\cdot\frac{100}{1}\
y=1500$$

anonymous · Answer

Oh, okay.

e.mccormick · Answer

The undefined part then becomes what they call an asymptote.  Vertical asymptotes are lines that can not be crossed.

anonymous · Answer

Alright. One more problem?

e.mccormick · Answer

Sure.

anonymous · Answer

Okay.

$$y = \frac{ -18 }{ x }$$

e.mccormick · Answer

Same principal.

e.mccormick · Answer

It just changes what quads because of the -.

anonymous · Answer

e.mccormick · Answer

The important thing for easy graphing of these are factors of 18.  Half points are not bad, but sometimes when you get down to weird numbers it just gets hard to graph nicely.  

18 9 6 3 2 1 are all factors of 18.  So they make the "easy" points this time. 1.8 is OK, just not as easy to graph as whole numbers and halfs.

anonymous · Answer

Okay.

e.mccormick · Answer

And you will get something like:|dw:1368216529907:dw|Not to scale this time, but I am sure that you get the point by now.

anonymous · Answer

For some reason -1.8,-10 and 1.8,10 aren't plotting right, I know you said it would be a bit harder.

e.mccormick · Answer

(-1.8,10),(1.8,-10)

anonymous · Answer

Yeah, I just realized I did it wrong, thanks.

e.mccormick · Answer

np.  Have fun!

anonymous · Answer

attachment

anonymous · Answer

Thanks for the help!

e.mccormick · Answer

Yah, not too terrible once you have the basic concept.