In the xy-plane, the line determined by the points (2,k) and (k,32) passes through the origin. Which of the following could be the value of k?

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Youngsun Lee

2019. március 6. 3:11

Here's the question: In the xy-plane, the line determined by the points (2,k) and (k,32) passes through the origin. Which of the following could be the value of k?

In part of the explanation, it says that since each expression gives the slope of the same line, it must be true that k/2=32/k.

I do not get which expression they're talking and where they got the k/2 from.

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Regina Litman

2019. március 6. 20:08
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Was this a multiple choice question? If so, please supply the possible values. Otherwise, I can't get to the k/2=32/k result.
Edward Killheffer

2019. március 10. 11:52
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By saying the line goes through each point and the origin, you can find the slope between each point and the origin using the slope formula or difference in the y's divided by the difference in the x's, you can write the slope between each point and the origin (0,0) and since they are all on the same line, you can set the slopes equal to each other. So you have

(k-0)/(2-0) = (32-0)/(k-0) or k/2=32/k
Regina Litman

2019. március 11. 2:50
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@Edward Killheffer, thank you for your answer! I had overlooked in the original post that the line passes through the origin.

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In the xy-plane, the line determined by the points (2,k) and (k,32) passes through the origin. Which of the following could be the value of k?

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