Find the slope of the linear function if f(2)=-9 and f(3)=9?

From enunciation, we conclude that we have two points (2,-9) and
(3,9) that are located on the graph of the linear function
f(x).

We'll write the linear function in the point slope
form:

f(x) = mx + n, where m is the slope and n is the y
intercept.

If f(2) = -9, we'll substitute x by 2 in the expression
of the linear function:

f(2) = 2m +
n

2m + n = -9

n = -9 - 2m
(1)

If f(3) = 9, we'll substitute x by 3 in the expression of the
linear function:

 f(3) = 3m + n

3m + n
= 9

n = 9 - 3m (2)

We'll put (1) =
(2):

-9 - 2m = 9 - 3m

We'll add 3m both
sides:

3m - 2m - 9 = 9

We'll add 9 both
sides:

m = 9 + 9

m =
18

The slope of the linear function is
m = 18.