f(1) = 8 is another way to say, x = 1, y = 8
f(5) = -4, is another way to say, x = 5, y = -4
so, what's the equation of a line that passes through (1, 8) and (5, -4)
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 8}})\quad
% (c,d)
&({{ 5}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-8}{5-1}\implies \cfrac{-12}{4}\implies -3[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=-3(x-1)
\\\\\\
y-8=-3x+3\implies y=-3x+3+8\implies y=-3x+11[/tex]
