Question #aa562

The slope of the secant line simplifies to $h + 11$ when $h \ne 0$.
To find the slope of the secant line, compute the "rise" $\Delta y$ over the "run" $\Delta x$.
$\frac{\Delta y}{\Delta x} = \frac{f \left(4 + h\right) - f \left(4\right)}{\left(4 + h\right) - 4} = \frac{{\left(4 + h\right)}^{2} + 3 \left(4 + h\right) + 7 - 35}{h}$
$= \frac{16 + 8 h + {h}^{2} + 12 + 3 h - 28}{h} = \frac{h \left(h + 11\right)}{h} = h + 11$ when $h \ne 0$.