Let's work through this step by step.

The table provided gives values for $x$ and $y$, which represent points on the line. To find the equation of the linear function, we can calculate the slope $m$ using the formula for the slope between two points:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

We can take two pairs of points from the table. Let's use (-5, 17) and (-2, 2):

$m = \frac{2 - 17}{-2 - (-5)} = \frac{-15}{3} = -5$

So, the slope is $m = -5$.

Next, we can use the slope-intercept form of a line, which is:

$y = mx + b$

We know $m = -5$. Now, to find the y-intercept $b$, we substitute one of the points from the table into the equation. Let's use the point (-2, 2):

$2 = -5(-2) + b$ $2 = 10 + b$ $b = 2 - 10 = -8$

So, the equation of the line is:

$y = -5x - 8$

The correct answer is D) $y = -5x - 8$.

Would you like more details or have any questions?

Here are 5 questions that expand on this:

1. How do you determine the slope if the two points have the same x-coordinate?
2. What happens if the points have the same y-coordinate? How does the slope change?
3. Could we use a different pair of points from the table to verify the slope?
4. How can you recognize a linear function just by looking at a table of values?
5. What does the slope tell us about the relationship between $x$ and $y$ in this function?

Tip: When solving linear equations, always check two points to ensure the calculated slope is consistent.