A line has slope 2k - 1 and passes through the points (1, 1) and (3, k+5). What is the value of k?

The slope through the two points is $\frac{(k + 5) - 1}{3 - 1} = \frac{k + 4}{2}$. This must equal the stated slope $2k - 1$, so $\frac{k + 4}{2} = 2k - 1$. Multiply by 2: $k + 4 = 4k - 2$. Then $6 = 3k$ and $k = 2$, choice B. Check: the second point is $(3, 7)$ and the slope is $\frac{7 - 1}{3 - 1} = 3$, which equals $2(2) - 1 = 3$. Choice A (3) gives slopes of 3.5 and 5. Choice C (1) gives 2.5 and 1. Choice D (4) gives 4 and 7. None matches.