Inverse Variation

<p>Could someone please explain this to me? I've read and read but all I understand is that as one variable increases, the other decreases. I get these wrong most of the time.</p>

<p>y = k/x where k is a constant and y increases as x decreases.</p>

<p>^ I second that. It looks like a curve with y —> Infinity as x ----> 0 and x —> infinity with y —> 0</p>

<p>Look at the equation:</p>

<p>y = k / x</p>

<p>k is a constant, x is the independent variable, and y is the dependent variable. If k is fixed, think about what happens to y as x increase. As x increases, k is being divided by a larger and larger number, thus making y smaller and smaller.</p>

<p>As x decreases, k is being divided by a smaller and smaller number, thus making y larger and larger.</p>

<p>Notice the graph: [graph</a> y = 1/x - Wolfram|Alpha](<a href=“graph y = 1/x]graph - Wolfram|Alpha”>graph y = 1/x - Wolfram|Alpha)</p>

<p>Real-world things that vary inversely are things like the force of gravity and distance. As you increase distance, gravity decreases. As you decrease distance, gravity is stronger.</p>

<p>I’d help you further if I was given a problem to solve.</p>

<p>Suppose the volume of a gas varies inversely with the pressure on the gas. If the volume is 10 at a pressure of 50 (i forgot the units), what is the volume at a pressure of 60?
Could you explain how this fits in with the explanation? Thanks for the help guys!</p>

<p>x = k/y</p>

<p>xy = k
10<em>50=k=500
x</em>60=k=500
x=500/60=8.33333333</p>

<p>It makes sense because pressure goes from 50 to 60, meaning it goes from 100% to 120% (it increases by 20%). Therefore, you want the volume to go from 120% to 100% so you divide by 1.2. 10/1.2 = 8.3333. Whatever CONSTANT you multiply ONE variable by, you divide the OTHER variable by.</p>

<p>oh thanks crazybandit, i think im starting to grasp this concept. Could you guys, if its not too much to ask, think of another question and explain that to me as well? thanks :)</p>

<p>Suppose the volume of a gas varies inversely with the pressure on the gas. If the volume is 10 at a pressure of 50 (i forgot the units), what is the volume at a pressure of 60? </p>

<p>y = k/x</p>

<p>Let y = volume
Let x = pressure
Let k = constant</p>

<p>v = k/p
10 = k/50
500 = k</p>

<p>Now when p = 60</p>

<p>v = k/p
v = k/60</p>

<p>We know that k is a constant so it does not change and is the same for all situations, so k = 500.</p>

<p>v = 500/60
v = 8.33</p>

<p>Is this even on the SATs? Not to be rude, I really don’t remember seeing anything like this. I remember learning it but not on the SATs.</p>

<p>They do ask questions with inverse proportionality on the SAT, yes. I have seen it on several practice tests.</p>

<p>Thanks a great deal Bassir! I really understand it now! Thanks all of you guys! now maybe i can finally start hitting the 800 mark :D</p>