To determine the equation of the line shown in the graph, follow these steps:

1. Identify the slope (m):

   • The slope is the "rise over run," or the change in $y$ divided by the change in $x$.
   • From the graph, the line passes through the points $(-3, 3)$ and $(0, 0)$.
   • Slope ($m$) = $\frac{\text{change in } y}{\text{change in } x} = \frac{3 - 0}{-3 - 0} = \frac{3}{-3} = -1$.

2. Determine the y-intercept ($b$):

   • The $y$-intercept is where the line crosses the $y$-axis.
   • From the graph, the line crosses the $y$-axis at $(0, 0)$. So, $b = 0$.

3. Write the equation:

   • The general slope-intercept form of a line is $y = mx + b$.
   • Substituting $m = -1$ and $b = 0$, the equation of the line is:

   $y = -x$

Let me know if you want additional explanation or assistance! Here are some related questions:

1. What does the slope of $-1$ represent in real-world scenarios?
2. How can we find the equation of a line if two points are not aligned on a grid?
3. What happens to the graph if the slope changes to a positive value?
4. How do we convert $y = -x$ into the general form $Ax + By + C = 0$?
5. Can we verify the equation using another point from the graph?

Tip: Always check the slope by ensuring the points used are accurate to avoid calculation errors!