Question

If f(2)=9 and f(-1)=14, write a linear function that fits this scenario. Be sure to use proper notation. HELP!!

Answer 1

The required linear function is: f(x) =
`$ (-5)/(3)x + (37)/(3) $`

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) =
`$ (-5)/(3) $`x +
`$ (37)/(3) $`.