Difference between revisions of "2003 AMC 12B Problems/Problem 9"
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| − | == Problem | + | == Problem == |
Let <math>f</math> be a linear function for which <math>f(6) - f(2) = 12.</math> What is <math>f(12) - f(2)?</math> | Let <math>f</math> be a linear function for which <math>f(6) - f(2) = 12.</math> What is <math>f(12) - f(2)?</math> | ||
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</math> | </math> | ||
| − | + | ==Solution== | |
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Since <math>f</math> is a linear function with slope <math>m</math>, | Since <math>f</math> is a linear function with slope <math>m</math>, | ||
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<cmath>f(12) - f(2) = m \Delta x = 4(12 - 2) = 30 \Rightarrow \text (D)</cmath> | <cmath>f(12) - f(2) = m \Delta x = 4(12 - 2) = 30 \Rightarrow \text (D)</cmath> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC12 box|year=2003|ab=B|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 23:37, 4 January 2014
Problem
Let 
be a linear function for which 
What is 
Solution
Since is a linear function with slope 
,
![\[m = \frac{f(6) - f(2)}{\Delta x} = \frac{12}{6 - 2} = 3\]](http://latex.artofproblemsolving.com/a/a/2/aa203aedcd175b965d80f840ac73c7f9356e3456.png)
![\[f(12) - f(2) = m \Delta x = 4(12 - 2) = 30 \Rightarrow \text (D)\]](http://latex.artofproblemsolving.com/c/d/c/cdc31f45fb1779b7e68669b031b809d19e97db40.png)
See Also
| 2003 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 8 |
Followed by Problem 10 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
