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?

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.

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

@Edward Killheffer, thank you for your answer! I had overlooked in the original post that the line passes through the origin.