Step 1 :Let the given points be \((-1,4)\) and \((5,-4)\).
Step 2 :To find the slope of the line that goes through the given points, we can use the formula: \[\text{slope} = \frac{y2 - y1}{x2 - x1}\]
Step 3 :Plug in the given points into the formula: \[\text{slope} = \frac{-4 - 4}{5 - (-1)}\]
Step 4 :Simplify the expression: \[\text{slope} = \frac{-8}{6}\]
Step 5 :Simplify the fraction to its simplest form: \[\text{slope} = -\frac{4}{3}\]
Step 6 :\[\boxed{\text{slope} = -\frac{4}{3}}\]