Recall that the equation of a line that passes through two points is given by the following formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Notice that the above formula gives us the equation of the line in point-slope form. Substituting the given values in the above formula, we get:
[tex]y-(-1)=\frac{-1-4}{2-8}(x-2).[/tex]Simplifying the above result, we get:
[tex]y+1=\frac{5}{6}(x-2).[/tex]Now, taking the above equation to its standard form, we get:
[tex]\begin{gathered} 6y+6=5(x-2), \\ 6y+6=5x-10, \\ 6y-5x=-10-6, \\ -5x+6y=-16. \end{gathered}[/tex]