To find the equation of a line we need to use the formula:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1,y1) is a point on the line. The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, the slope of the line (using the first two points on the table) is:
[tex]m=\frac{6-1}{2-1}=\frac{5}{1}=5[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-1=5(x-1) \\ y-1=5x-5 \\ y=5x-5+1 \\ y=5x-4 \end{gathered}[/tex]Therefore, the line is:
[tex]y=5x-4[/tex]