Circles SAT question

Choice A is correct. A line that's tangent to a circle is perpendicular to the radius of the circle at the point of tangency. It's given that the circle has its center at $(-4,-6)$ and line $k$ is tangent to the circle at the point $(-7,-7)$. The slope of a radius defined by the points $(q,r)$ and $(s,t)$ can be calculated as $\frac{t-r}{s-q}$. The points $(-7,-7)$ and $(-4,-6)$ define the radius of the circle at the point of tangency. Therefore, the slope of this radius can be calculated as $\frac{(-6)-(-7)}{(-4)-(-7)}$, or $\frac{1}{3}$. If a line and a radius are perpendicular, the slope of the line must be the negative reciprocal of the slope of the radius. The negative reciprocal of $\frac{1}{3}$ is $-3$. Thus, the slope of line $k$ is $-3$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the slope of the radius of the circle at the point of tangency, not the slope of line $k$.

Choice D is incorrect and may result from conceptual or calculation errors.