You should know that you may find the slope of the line converting the equation of the function to the slope intercept form such that:
`y = mx + n`
m represents the slope of the line `y = mx + n`
Reasoning by analogy, you need to convert the equation of the function `f(x) = -2x - 9` to the form mentioned above such that:
`y = -2x - 9`
Notice that the slope is given by the leading coefficient such that:
`m = -2`
Hence, evaluating the slope of the given function yields `m=-` 2.
If we look at f(x)= -2x-9 if x<-3
-4 if -3<x<1
x-5 if 1<x<4
-3/2x+3 if 4<x then we know that when x is between -3 and 1, f(x)=-4. If you graphf(x)=-4 you will see that it will simply be a horizontal line. And the slope of any horizontal line will ALWAYS be zero. So the slope of the function over the interval -3<x<1 is zero.