4/26/10

Test 1 Section 3 - #15 (page 400)

I love this question because it's susceptible to multiple techniques.  GUESSTIMATE makes the most sense:

You know this slope is negative just from looking at it: it goes down from left to right.  So that leaves us with only (A) and (B) before we even look very closely.  When we do look more closely, we can tell that this slope isn't very steep...its run is bigger than its rise, if you will.  The only answer that really makes sense is (B): -1/2.

Let's confirm that by putting our answer back into the question.  This is the other way we could have solved it, BACKSOLVE (using the slope formula).

Slope is rise over run, or:
We're luck here that our line goes through the origin, so we can replace y1 and x1 with 0.  Basically, we're looking, then, for an answer choice in the form of y/x that fits our diagram at point A.  Again, we're basically back to guesstimating here, in that the way we make our decision is that (-2,1) looks more like point A than (-1,2) does.  Either way, our answer is (B).

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