The given values are f(0)=7, and f(3)=1.
The general equation of the linear function is
[tex]f(x)=mx+b[/tex]
From the value f(0)=7, subsitute x=0 and f(0)=7 in the general equation of the linear function as follows:
[tex]f(0)=m(0)+b[/tex][tex]7=b[/tex]
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:
[tex]f(3)=m(3)+7[/tex]
Here f(3)
[tex]1=3m+7[/tex]
Transferring 7 to the left-hand side, we get
[tex]1-7=3m[/tex][tex]-6=3m[/tex]
Transferring 3 to the left-hand side, we get
[tex]-\frac{6}{3}=m[/tex][tex]-2=m[/tex]
Substitute m=-2 and b=7 in the general equation of the linear function as follows:
[tex]f(x)=-2x+7[/tex]
Hence the required linear function is f(x)= -2x+7.
