SAT Math Tutorial
Direct Variation vs. Inverse Variation
Intro
The SAT often asks questions about direct variation and inverse variation. These questions use wording like “…varies directly with…”, “…varies inversely with…”, “…is directly proportional to…” and “…is inversely proportional to…”
The formulas for direct and inverse variation are as follows.
Direct Variation
As one variable increases, the other variable increases proportionately.
![\[ y=kx \]](https://www.theknowledgeroundtable.com/wp-content/ql-cache/quicklatex.com-e2099af44c98f09edb21d85dbdab6c86_l3.png "Rendered by QuickLaTeX.com")
Inverse Variation
As one variable increases, the other variable decreases proportionately.
![\[ y=\frac{k}{x} \]](https://www.theknowledgeroundtable.com/wp-content/ql-cache/quicklatex.com-3dbdcd281c354884545d14b03a549305_l3.png "Rendered by QuickLaTeX.com")
Here is a typical SAT variation problem.
Sample Problem
when 
, then what is the value of Solution
The first step for this problem is to determine whether to use the direct variation formula or the inverse variation formula.
In this case, the problem states that “
varies directly with 
.” Thus, the relationship between and is a direct one, requiring the direct variation formula, 
.
Next, find the value for 
by substituting the appropriate values for and into the direct variation formula.
Once the value of is determined, substitute it into to see the true relationship between and .
![\[ y=4.8x \]](https://www.theknowledgeroundtable.com/wp-content/ql-cache/quicklatex.com-091f3885447a9e042ccc7b3f73321f16_l3.png "Rendered by QuickLaTeX.com")
Finally, the question asks for “the value of when 
.” So substitute 48 for in the equation above and solve for .
Thus, the answer is 
.
Challenge Questions
How would the answer change if the question stated that “ varies inversely with ?” What if it stated that “ varies inversely as the square of ?”
About The Author
|
2 reviews |
| Math Expert And SAT Instructor |
| Jared, founder of The Knowledge Roundtable, is passionate about the advancement of knowledge. He has a B.S. in astronomy and physics from UMass and an MBA in Advanced Financial Analytics, also from UMass. He has a day job as a Data Scientist in Boston. He has over 500 hours of tutoring experience... |
Suggested Tutors for SAT Math Help
