Question

determine whether the relation shown in the table is a direct variation, and inverse, or neither.
x= 10, 15, 20, 25
y= 1/2, 1/3, 1/4, 1/5

Answer 1

help me please @whpalmer4

Answer 2

Direct variation is when changes in one quantity cause the other quantity to change in direct proportion. In math terms, we can say that if \(y\) varies directly with \(x\), then \[y = kx\]where \(k\) is a constant called the constant of variation. If this looks like the slope of a line to you, give yourself a pat on the back! If we double \(x\), then \(y\) will double. If we divide \(x\) by \(3\), then \(y\) will be divided by \(3\).

Indirect variation is when changes in one quantity cause the other quantity to change in the other direction, so to speak. For example, if \(y\) varies indirectly with \(x\), \(x\) getting larger means \(y\) gets smaller, and vice versa. We can write this sort of variation as \[y=\frac{k}{x}\]

Answer 3

i think it is a Inverse variation
would the equation be this
y = 5/x


am i correct?? o.0

Answer 4

So, looking at the data, just observing the trends as \(x\) increases, does this look like it could be direct or indirect variation?

Answer 5

Well, here's how you find out. Pick a pair of \(x,y\), and write the equation:

\[\frac{1}{2} = \frac{k}{10}\]Solving for \(k\), we get \(k=5\). So far, so good, that's what you have. Now we need to try some other data points, to see if they fit that equation. If they don't, it isn't indirect variation between \(x\) and \(y\).

Let's try \(20,\frac{1}{4}\):

\[\frac{1}{4} = \frac{5}{20}\checkmark\]
Okay, if that hadn't worked, we would know we don't have indirect variation.

Answer 6

kool so i was right!!! XP

Answer 7

Eyeballing the rest of them, it appears that they all satisfy the equation, so that is indirect variation, with the constant of variation = \(5\).

Answer 8

thank you so much!!! your LIFE SAVER

Answer 9

Now, it's possible that you could have a set of data which was indirect variation but didn't fit, if the variation was with some other quantity. In physics, for example, many things vary indirectly with the square of the distance between them, rather than with the distance. So you might look at a table of data, and say "hmm, y gets smaller as r gets bigger, must be indirect variation between y and r", go find the constant, and when you test it on the other data, it doesn't fit. At that point, you would perhaps be rash to conclude that this meant it isn't indirect variation — it just isn't indirect variation between \(y\) and \(r\). A next step would be to consider indirect variation between \(y\) and \(r^2\), which would look like \[y = \frac{k}{r^2}\] and might fit the data perfectly!

Answer 10

You know me, always trying to cram just a little bit more information in your brain, whether you wanted it or not :-)