Question

Find f(x) if f is a linear function such that f(6)=4 and f(−5)=−6 .

Answer 1

f(x) =
`(10)/(11)`x
`-(16)/(11)`

Explanation:

The format of the linear function f(x) is ax + b. Thus, we can list the following equations:

4 = 6a + b .... (1)

-6 = -5a + b .... (2)

We can use the first equation to subtract the second equation getting: 10 = 11a. This means a =
`(10)/(11)`. From that, if we plug in the value of a into the first equation, we get 4 =
`(60)/(11)` + b, so b =
`-(16)/(11)`. Thus, f(x) =
`(10)/(11)`x
`-(16)/(11)`