Inverse and Direct Proportionality

Test Preparation SAT Preparation
1

<p>I don't get this question...</p>

<p>If x does not equal 0 and x is inversely proportional to y, which of the following is directly proportional to 1/(x^2)?</p>

<p>A) -1/(y^2)
B) 1/(y^2)
C) 1/y
D) y
E) y^2</p>

<p>Answer is E</p>

2

<p>I understand that inverse proportionality would be yx=C and direct would be y/x=C (C is a constant)</p>

3

<p>so inverse formula is x=k/y, thus if you square both sides, x^2=k^2/y^2, if you cross multiply and divide, y^2=k^2/x^2. Only one that is that form is E.</p>

4

<p>I don’t get how the inverse and direct proportions relate though :/</p>

5

<p>Hopefully someone can help me out D:</p>

6

<p>The main ideas are:</p>

<p>If two things are DIRECTLY proportional, you can express the relationship</p>

<p>as Y = Constant times X </p>

<p>which is also equivalent to Y/X = constant. That’s why you solve those kinds of problems by setting up a proportion.</p>

<p>If the two things are INVERSELY proportional, then it’s:</p>

<p>Y = Constant divided by X</p>

<p>which is also equivalent to XY = constant.</p>

<p>I have a summary of these relationships on my website. It’s designed to help my physics students but it may help you to review these specific concepts.</p>

<p>[Mr</a>. Keller’s Physics Class Info](<a href=“http://holmdelschools.org/faculty/pkeller/Summer%20Relationships.htm]Mr”>http://holmdelschools.org/faculty/pkeller/Summer%20Relationships.htm)</p>

<p>PLEASE NOTE – I am NOT recommending this link as a general SAT resource! There are no ads on that site and I am not trying to drive traffic that way! It just addresses this very specific question that OP has asked.</p>

7

<p>I understand the formulas and why they are so, but what I want to know is how y^2 is directly proportional to 1/x^2 while x and y are still inversely proportional</p>

8

<p>If two things are directly proportional, then thing1 = constant times thing2.</p>

<p>As gertrudedtrumpet showed above, you can start with</p>

<p>y = k/x (because you know that they are inversely proportional)</p>

<p>and square both sides to get</p>

<p>y^2 = k^2/x^2</p>

<p>But k^2 is just a constant so now you have</p>

<p>y^2 = constant times 1/x^2</p>

<p>Think of y^2 as thing1 and 1/x^2 as thing2.</p>

<p>Hope that helps…</p>

9

<p>Ahhhh that makes sense. I always see the inverse and direct with x and y on one side and the constant on the other because it’s more logical to me. Thank you!</p>