A line has an x-intercept of -3 and a y-intercept of 9. What is the slope of the line?

The intercepts give two points: the $x$-intercept $-3$ is $(-3, 0)$ and the $y$-intercept 9 is $(0, 9)$. The slope is the rise over the run: $\frac{9 - 0}{0 - (-3)} = \frac{9}{3} = 3$, choice D. The line rises as it moves right, so the slope is positive. Choice A ($-3$) has the wrong sign, which happens when the subtraction $0 - (-3)$ is treated as $-3$. Choice B ($\frac{1}{3}$) inverts the ratio, giving run over rise. Choice C ($-\frac{1}{3}$) combines both errors. Check with the equation $y = 3x + 9$, which gives 0 at $x = -3$.