Step 1 :The slope of a line that contains two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Step 2 :Substitute the given points into this formula to find the slope: \[ m = \frac{-8 - (-\frac{5}{2})}{3 - (-3)} \]
Step 3 :The slope of the line is a negative decimal number. To match it with the options given in the question, we need to convert this decimal into a fraction.
Step 4 :The slope of the line that contains the points \((-3,-\frac{5}{2})\) and \((3,-8)\) is \(\boxed{-\frac{11}{12}}\).