Test 10 Question 23

I’m going to give you two ways to go on this one. First, you can get it pretty quickly with a combination of plugging in and backsolving. Plug in a nice easy number for a; say a=2. Then the table looks like this:

Now the backsolving part. Just start trying answer choices! Choice A, with our plugged in value for a, says x+2y=2. Does that work with all the values we have? Sure does! 2+2(0)=2, 6+2(-2)=2, and 10+2(-4)=2. So choice A is the answer.

If you don’t like life-saving, score-boosting techniques, though, you can also do this problem with algebra.

Pick two ordered pairs from the table and use them to calculate the slope of the line. I’m going to use (a,0) and (3a,-a).


So we have the slope. Now plug any of the points into slope-intercept form to find the intercept (b). I’ll use (a, 0).


OK, so now we have a slope of -\dfrac{1}{2} and a y-intercept of \dfrac{a}{2}. In slope-intercept form, the equation of the line is y=-\dfrac{1}{2}x+\dfrac{a}{2}.

None of the answer choices look like that, but with a little manipulation we can get there. Start by multiplying by 2 to get rid of the fractions.


Boom–choice A it is.

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