Question

y=f(x)=4/x. Use algebra to find a simplified rational expression for the slope of the line between (3, f(3)) and (3+h, f(3+h))??

Answer 1

\[\frac{f(3+h)-f(3)}{(3+h)-3}=\frac{\frac{4}{3+h}-\frac{4}{3}}{h}=\frac{\frac{12-4(3+h)}{3(3+h)}}{h}=\frac{-h}{3h(3+h)}=\frac{-1}{3(3+h)}\]

Answer 2

You lost a 4; 12-4(3+h) = 12-12-4h= -4h

Answer 3

Keep in mind that the slope is provided by:
\[\frac{rise}{run}\]

So, that is exactly what Satellite provided. The numerator provides the change in rise (delta y) and the denominator provides the change in run (delta x).