Answer:
The required linear function is: f(x) = [tex]$ \frac{-5}{3}x + \frac{37}{3} $[/tex]
Step-by-step explanation:
We are given that f(x) is a linear function and it takes the value 9 when x = 2 and 14 when x = -1.
Now the general form of any linear function is: f(x) = ax + b.
Substituting these values in the general form we get:
f(2) = 9 = 2a + b
f(-1) = 14 = -a + b
Solving these two equations we get:
b = 37/3
Substituting this in the second equation to find 'a'.
a = -5/3
Therefore, the function f(x) = [tex]$ \frac{-5}{3} $[/tex]x + [tex]$ \frac{37}{3} $[/tex].
