SAT Mathematics Practice Test 3

The line passes through the origin, (2, k), and (k, 32).
Any two of these points can be used to find the slope of the line.
Since the line passes through (0, 0) and (2, k), the slope of the line is equal to $\frac{\mathit{k}-0}{2-0}=\frac{\mathit{k}}{2}$
Similarly, since the line passes through (0, 0) and (k, 32), the slope of the line is equal to $\frac{32-0}{\mathit{k}-0}=\frac{32}{\mathit{k}}$
Since each expression gives the slope of the same line, it must be true that $\frac{\mathit{k}}{2}=\frac{32}{\mathit{k}}$
Multiplying each side of $\frac{\mathit{k}}{2}=\frac{32}{\mathit{k}}$ by $2\mathit{k}$ gives ${\mathit{k}}^2=64$
from which it follows that $\mathit{k}=8$ or $\mathit{k}=-8$
Therefore, of the given choices, only8 could be the value of k.
Choices A, B, and D are incorrect and may be the result of calculation errors