Question

Write a linear function f with the given values f(0)=7f(3)=1

Answer 1

The given values are f(0)=7, and f(3)=1.

The general equation of the linear function is

`f(x)=mx+b`

From the value f(0)=7, subsitute x=0 and f(0)=7 in the general equation of the linear function as follows:

`f(0)=m(0)+b`
`7=b`

From the value f(3))=1, substitute x=3 , f(3)=1, and b=7 in the general equation of the linear function as follows:

`f(3)=m(3)+7`

Here f(3)

`1=3m+7`

Transferring 7 to the left-hand side, we get

`1-7=3m`
`-6=3m`

Transferring 3 to the left-hand side, we get

`-(6)/(3)=m`
`-2=m`

Substitute m=-2 and b=7 in the general equation of the linear function as follows:

`f(x)=-2x+7`

Hence the required linear function is f(x)= -2x+7.