Given:
The function is
[tex]f(x)=-5x-7[/tex]
To find:
The rate of change of the given function.
Solution:
We have,
[tex]f(x)=-5x-7[/tex] ...(i)
It is a linear function because the degree or power of x in this function is 1.
Slope of a linear function is always constant.
The slope intercept form of a linear function is
[tex]f(x)=mx+b[/tex] ...(ii)
where, m is slope and b is y-intercept.
On comparing (i) and (ii), we get
[tex]m=-5[/tex]
It means, the function has a constant rate of change, decreasing for all x at a rate of 5.
Therefore, the correct option is D.
