To find the equation of the line in slope-intercept form, we need two key pieces of information:

1. The slope (m) of the line.
2. The y-intercept (b), which is where the line crosses the y-axis.

Step 1: Find the slope (m)

The slope of a line is calculated using the formula:

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

Looking at the graph:

• One point on the line is $(-9, 11)$.
• Another point is $(-6, 8)$.

Using these two points: $m = \frac{{8 - 11}}{{-6 - (-9)}} = \frac{{-3}}{{3}} = -1$

So, the slope of the line is $m = -1$.

Step 2: Find the y-intercept (b)

The y-intercept is the point where the line crosses the y-axis. In the graph, the line crosses the y-axis at $y = 2$. So, $b = 2$.

Step 3: Write the equation

Now, we can use the slope-intercept form equation:

$y = mx + b$

Substitute $m = -1$ and $b = 2$:

$y = -x + 2$

Thus, the equation of the line in fully simplified slope-intercept form is:

$\boxed{y = -x + 2}$

Would you like further details or explanations?

Here are some related questions to expand your understanding:

1. What is the formula for calculating the slope of a line?
2. How do you find the slope from two points on a line?
3. What is the significance of the y-intercept in the slope-intercept form?
4. How do you determine if a line is increasing or decreasing from its slope?
5. What is the relationship between slope and parallel lines?

Tip: Remember, when the slope is negative, the line decreases as it moves from left to right.