To find the equation of the linear function represented by the table in slope-intercept form ($y = mx + b$), we need to:

1. Calculate the slope (m): The slope can be found using the formula:

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

Using two points from the table, for example, $(x_1, y_1) = (11, -9)$ and $(x_2, y_2) = (22, -13)$:

$m = \frac{-13 - (-9)}{22 - 11} = \frac{-13 + 9}{11} = \frac{-4}{11}$

Thus, the slope $m = -\frac{4}{11}$.

2. Find the y-intercept (b): Once we have the slope, we can use the slope-intercept form to find $b$. We know that $y = mx + b$, so we can plug in one point and the slope into this equation to solve for $b$. Let's use $(x_1, y_1) = (11, -9)$:

$-9 = \left( -\frac{4}{11} \right) \times 11 + b$

Simplifying:

$-9 = -4 + b$

Solving for $b$:

$b = -9 + 4 = -5$

So, the equation of the linear function is:

$y = -\frac{4}{11}x - 5$

Summary:

The equation of the linear function in slope-intercept form is: $y = -\frac{4}{11}x - 5$

Do you need any more details or clarifications on how this equation was derived?

Additional Questions:

1. How do you calculate the slope from a table of values?
2. What happens if the points in the table don't form a straight line?
3. How would you graph this linear equation?
4. What is the significance of the slope in real-world contexts?
5. How do you interpret the y-intercept in this equation?

Tip: When calculating the slope, always use two points from the table and ensure you subtract the $y$-values in the correct order to avoid a negative sign mistake.