What is the slope of a line perpendicular to the line containing the points $(4,-7)$ and $(-5,-1)$? Express your answer as a common fraction.
To find the slope of a line, I need to use the slope formula: $m = \frac{y_2-y_1}{x_2-x_1}$. The line containing the points $(4,-7)$ and $(-5,-1)$ has a slope of $m = \frac{-1-(-7)}{-5-4} = \frac{6}{-9} = -\frac{2}{3}$. A line perpendicular to this line will have a slope that is the negative reciprocal of $-\frac{2}{3}$. The negative reciprocal of $-\frac{2}{3}$ is $\frac{3}{2}$. So the slope of a line perpendicular to the line containing the points $(4,-7)$ and $(-5,-1)$ is $\frac{3}{2}$. 