The graph shows a linear function passing through the points $(-6, 6)$ and $(-3, 5)$. I will calculate the equation of the line based on these points.

Step 1: Find the slope ($m$) of the line

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points $(-6, 6)$ and $(-3, 5)$: $m = \frac{5 - 6}{-3 - (-6)} = \frac{-1}{-3 + 6} = \frac{-1}{3}$

The slope of the line is: $m = -\frac{1}{3}$

Step 2: Use the point-slope form to find the equation

The point-slope form of a linear equation is: $y - y_1 = m(x - x_1)$ Using the point $(-6, 6)$ and the slope $m = -\frac{1}{3}$, substitute into the equation: $y - 6 = -\frac{1}{3}(x - (-6))$ Simplify: $y - 6 = -\frac{1}{3}(x + 6)$ $y - 6 = -\frac{1}{3}x - 2$ $y = -\frac{1}{3}x + 4$

Final Equation

The equation of the line is: $y = -\frac{1}{3}x + 4$

Would you like further details about the process or additional explanations?

Here are 5 related questions:

1. What is the y-intercept of this line and how is it interpreted?
2. How would the graph change if the slope was positive instead of negative?
3. Can you determine the x-intercept of the line from its equation?
4. How do we rewrite this equation in standard form ($Ax + By = C$)?
5. What happens to the equation if the line passes through the origin?

Tip: The slope tells you how much $y$ changes for every unit increase in $x$. Understanding this helps interpret linear relationships in data.