2016 AMC 12A Problems/Problem 7
Problem
Which of these describes the graph of ?
Solution 1
The equation tells us or . generates two lines and . is another straight line. The only intersection of and is , which is not on . Therefore, the graph is three lines that do not have a common intersection, or
Solution 2
If , then dividing both sides of the equation by gives us . Rearranging and factoring, we get . If , then the equation is satisfied. Thus either , , or . These equations can be rearranged into the lines , , and , respectively. Since these three lines are distinct, the answer is .
Solution 3
Subtract on both sides of the equation to get . Factoring gives us , so either , , or . Continue on with the second half of solution 2.
Diagram:
See Also
2016 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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