You may use the slope equation, such that:
`m = (y_2 - y_1)/(x_2 - x_1)` (`m` represents the slope of the line)
The problem provides `(x_1,y_1) = (2,-9)` and `(x_2,y_2) = (3,9)` , hence, you may substitute the given values of coordinates in slope equation, such that:
`m = (9 - (-9))/(3 - 2) => m = 18/1 => m = 18`
Hence, evaluating the slope of the line that passes through the points `(2,-9)` and `(3,9)` yields `m = 18.`
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.