Since the function is linear, we know that it is a line.
Let's use points (2,1) and (4,4) to calculate the slope:
[tex]m=\frac{4-1}{4-2}\rightarrow m=\frac{3}{2}[/tex]
We can use this slope, point (2,1) and the slope-intercept form to find an equation, as following:
[tex]\begin{gathered} y-1=\frac{3}{2}(x-2) \\ \\ y-1=\frac{3}{2}x-3 \\ \\ \Rightarrow y=\frac{3}{2}x-2 \end{gathered}[/tex]
Thereby, our function would be:
[tex]f(x)=\frac{3}{2}x-2[/tex]
To fill the table,
[tex]\begin{gathered} -2=\frac{3}{2}x-2 \\ \rightarrow0=\frac{3}{2}x \\ \\ \Rightarrow x=0 \end{gathered}[/tex][tex]\begin{gathered} f(x)=\frac{3}{2}(-2)-2 \\ \Rightarrow f(x)=-5 \end{gathered}[/tex]
The complete table would be:
