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\begin{aligned} m &=\frac{\Delta y}{\Delta x}=\frac{(2+h)^{2}-4}{(2+h)-2} \\ &=\frac{\left\{4+4 h+h^{2}\right\}-4}{h}=\frac{4 h+h^{2}}{h}=\frac{h(4+h)}{h}=4+h. \end{aligned}