Question

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?

Answer 1

a = 10/3.

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.