A line has a slope of 3/5. Through which two points could this line pass?
A. (-9, 7) and (4, -3)
B. (-7, -2) and (5, 21)
C. (8, 1) and (5, 0)
D. (6, 3) and (11, 6)
We can use the formula for the slope between two points $(x_1,y_1)$ and $(x_2,y_2),$ which is: $$m = \frac{y_2 - y_1}{x_2 - x_1}.$$If a line has a slope of $\frac{3}{5},$ then we can consider $m = \frac{3}{5}.$
Using the formula for the slope between two points, we can relate $\frac{3}{5}$ to the coordinates of two points $(x_1,y_1)$ and $(x_2,y_2)$: $$\frac{3}{5} = \frac{y_2 - y_1}{x_2 - x_1}.$$We want to find points $(x_1,y_1)$ and $(x_2,y_2)$ that satisfy this equation.
We can check each set of points given in the answer choices:
[A. $(-9, 7)$ and $(4, -3).$] We see that $$\frac{3}{5} = \frac{-3 - 7}{4 - (-9)} = \frac{-10}{13}.$$The slope between $(-9,7)$ and $(4,-3)$ is not $\frac{3}{5},$ so this answer choice does not work.
[B. $(-7, -2)$ and $(5, 21).$] We see that $$\frac{3}{5} = \frac{21 - (-2)}{5 - (-7)} = \frac{23}{12}.$$The slope between $(-7,-2)$ and $(5,21)$ is not $\frac{3}{5},$ so this answer choice does not work.
[C. $(8,1)$ and $(5,0).$] We see that $$\frac{3}{5} = \frac{0 - 1}{5 - 8} = \frac{1}{-3} = -\frac{1}{3}.$$The slope between $(8,1)$ and $(5,0)$ is not $\frac{3}{5},$ so this answer choice does not work.
[D. $(6,3)$ and $(11,6).$] We see that $$\frac{3}{5} = \frac{6 - 3}{11 - 6} = \frac{3}{5}.$$The slope between $(6,3)$ and $(11,6)$ is $\frac{3}{5},$ so this answer choice does work.
Therefore, the correct answer is $\boxed{\text{(D) } (6,3) \text{ and } (11,6)}.$