[tex]\bf \begin{array}{|c|c|c|c|c|c|ll} \cline{1-6} x&0&1&2&3&4\\ \cline{1-6} g(x)&0&5&15&20&?\\ \cline{1-6} \end{array}~\hfill slope = m = \cfrac{rise}{run} \implies \stackrel{\textit{average rate of change}}{\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}} \\\\[-0.35em] ~\dotfill\\\\ 1\leqslant x \leqslant 4\implies \begin{cases} x=1\\ x=4 \end{cases}\implies \cfrac{g(4)-g(1)}{4-1}=\stackrel{\downarrow }{16}\implies \cfrac{?-5}{3}=16 \\\\\\ ?-5=48\implies ?=53[/tex]
