The rate of change of a function can be modeled with the following expression:
[tex]\frac{\Delta{k{x)}}{\Delta{x}} [/tex]
Where Δx is the change in x value, and Δk(x) is the corresponding change in k(x). We're given the two extremes of x, so we can calculate the change in x to be
[tex]\Delta{x}=-4-(-14)=10[/tex]
To find the change in k(x), we can calculate the values of k(x) at x = -14 and x = -4 and find the difference between them:
[tex]k(-14)=5(-14)-19=-70-19=-89\\ k(-4)=5(-4)-19=-20-19=-39\\ \Delta{y}=k(-14)-k(-4)=-89-(-39)=-50[/tex]
So, the rate of change for the function from x = -14 to x = -4 is
[tex] \frac{\Delta{y}}{\Delta{x}}= \frac{-50}{10}=-5 [/tex]
