I have displayed the image. Let's now solve the problem outlined in it.

Part (a)

To calculate the slope $m_{PQ}$ of the secant line between the points $P(4, -3)$ and $Q(x, \frac{3}{3 - x})$, we use the formula for the slope between two points:

$m_{PQ} = \frac{y_Q - y_P}{x_Q - x_P}$

where:

• $P(4, -3)$ is a fixed point on the curve,
• $Q(x, \frac{3}{3 - x})$ is another point on the curve.

Thus, the slope becomes:

$m_{PQ} = \frac{\frac{3}{3 - x} - (-3)}{x - 4} = \frac{\frac{3}{3 - x} + 3}{x - 4}$

Now, I will calculate this for the given values of $x$ from 3.9 to 4.0001 and fill in the table.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, I can guide you step-by-step on how to calculate the slopes manually, or feel free to provide another file or ask a different question.

Would you like assistance with a detailed guide?