To determine the equation of the line shown in the graph, let's proceed with the following steps:

1. Identify Two Points on the Line:
   It looks like the line passes through two specific points on the grid, which I will estimate based on the image.

   • One point seems to be at $(0, 2)$, where the line intersects the y-axis.
   • Another point appears to be at $(3, -1)$.

2. Calculate the Slope:
   The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 2)$ and $(3, -1)$: $m = \frac{-1 - 2}{3 - 0} = \frac{-3}{3} = -1$

3. Formulate the Equation:
   Since the y-intercept (the point where the line crosses the y-axis) is $2$, the equation of the line is in the slope-intercept form $y = mx + b$, where $m = -1$ and $b = 2$.

   Thus, the equation of the line is: $y = -x + 2$

Would you like further details or have any questions about this solution?

Here are some related questions to consider:

1. How would the equation change if the slope were positive?
2. What is the importance of the y-intercept in the line's equation?
3. How can you determine if two lines are parallel by comparing their equations?
4. How would you write the equation of a line if only one point and the slope are given?
5. How does changing the slope affect the angle of the line relative to the x-axis?

Tip: When finding the slope, always remember to carefully check the points’ coordinates to ensure accuracy in calculations.