What is the slope of the linear function if f(2)=-6 and f(-2)=4 ?

From enunciation, we conclude that we have two points
(2,-6) and (-2,4) that are located on the graph of the linear function
f(x).

We'll put 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) = -6, we'll substitute x by 2 in the
expression of the linear function:

f(2) = 2m +
n

2m + n = -6

n = -6 - 2m
(1)

If f(-2) = 4, we'll substitute x by -2 in the
expression of the linear function:

f(-2) = -2m +
n

-2m + n = 4

n = 4 + 2m
(2)

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

-6
- 2m  = 4 + 2m

We'll move 2m to the
left:

-2m - 2m - 6 = 4

We'll
add -6 both sides:

-4m =
10

m =
10/-4

m =
-5/2

The slope of the linear
function is m = -5/2.