anonymous
  • anonymous
Can someone show me how to graph xy = 15?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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e.mccormick
  • e.mccormick
Find y, graph a few points, like the y intercept. and watch out for x=0.
e.mccormick
  • e.mccormick
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
  • e.mccormick
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.

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anonymous
  • anonymous
Okay.
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e.mccormick
  • e.mccormick
Then play connect the dots. Remember, you can't cross either the x or y axis.
e.mccormick
  • e.mccormick
(1,15), (15,1), (-1,-15), (-15,-1) are also there, so you have an idea what happens to the tails.
e.mccormick
  • e.mccormick
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
  • anonymous
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e.mccormick
  • e.mccormick
Yep! https://www.desmos.com/calculator/n7xd8g8ojy
anonymous
  • anonymous
Thanks!
anonymous
  • anonymous
Could you help me with one more?
e.mccormick
  • e.mccormick
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
  • anonymous
Not exactly sure.
anonymous
  • anonymous
Because it is undefined?
e.mccormick
  • e.mccormick
\(y=\frac{15}{x}\) 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
  • anonymous
Oh, okay.
e.mccormick
  • e.mccormick
The undefined part then becomes what they call an asymptote. Vertical asymptotes are lines that can not be crossed.
anonymous
  • anonymous
Alright. One more problem?
e.mccormick
  • e.mccormick
Sure.
anonymous
  • anonymous
Okay. \[y = \frac{ -18 }{ x }\]
e.mccormick
  • e.mccormick
Same principal.
e.mccormick
  • e.mccormick
It just changes what quads because of the -.
anonymous
  • anonymous
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e.mccormick
  • e.mccormick
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
  • anonymous
Okay.
e.mccormick
  • e.mccormick
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
  • anonymous
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
  • e.mccormick
(-1.8,10),(1.8,-10)
anonymous
  • anonymous
Yeah, I just realized I did it wrong, thanks.
e.mccormick
  • e.mccormick
np. Have fun!
anonymous
  • anonymous
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anonymous
  • anonymous
Thanks for the help!
e.mccormick
  • e.mccormick
Yah, not too terrible once you have the basic concept.

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