There exists a linear function f (x) such that f (6) = 8, f (2) = 20, and f (a) = 16. What is the value of 2a?

a = 10/3.

Step-by-step explanation:

We write the linear function as follows:

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

f (6) = 6m + b = 8

f (2) = 2m + b = 20 Subtracting these 2 equations:

4m = - 12

m = - 3.

and - 3 * 2 + b = 20 so:

b = 20 + 6 = 26.

So we have the linear function:

f (x) = - 3 x + 26

f (a) = 16 = - 3 a + 26

-3 a = 16-26

a = - 10 * - 3 = 10/3.