To solve this problem, let's proceed step by step:

1. Determine the slope of the given linear function from the table: Using two points from the table $(-4, 2)$ and $(0, -3)$, the slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 2}{0 - (-4)} = \frac{-5}{4}.$ Thus, the slope of the given function is $-\frac{5}{4}$.

2. Compare the slopes of the options:

   • Option A: $y = x + 3$, slope $m = 1$. (Greater than $-\frac{5}{4}$.)
   • Option B: From the graph, the slope appears steeper than $-\frac{5}{4}$. (Greater than $-\frac{5}{4}$.)
   • Option C: $y = -\frac{5}{4}x - 3$, slope $m = -\frac{5}{4}$. (Equal to the given slope.)
   • Option D: From the graph, the slope is less steep, closer to $m = -\frac{1}{2}$. (Lesser than $-\frac{5}{4}$.)

3. Conclusion: The relationship with a lesser slope than the given function is Option D.

If you have further questions or need more details, feel free to ask.

Here are some follow-up questions for further exploration:

1. How is slope defined in linear functions, and why is it important?
2. Could you explain why a steeper graph has a greater absolute slope?
3. How does the slope affect the appearance of a graph?
4. What are the practical applications of comparing slopes in real-life scenarios?
5. How can you confirm a slope using multiple points from a table or graph?

Tip: When analyzing slopes, always compare the steepness and direction (positive or negative) of the lines.