you can either graph this or plug in values.
[tex]f(x)=3+\frac{1}{3}x[/tex]
[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]
[tex]\therefore[/tex] we can conclude that this function is linear.
Also here is a graph
