To determine the equation of the line in the given graph, let us analyze the graph and extract the key features:

1. Identifying two points on the line:

   • From the graph, the line passes through these points:
     • Point 1: $(0, -2)$ (the y-intercept).
     • Point 2: $(2, -4)$.

2. Calculating the slope ($m$): The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of the two points: $m = \frac{-4 - (-2)}{2 - 0} = \frac{-4 + 2}{2} = \frac{-2}{2} = -1$

3. Writing the equation of the line: Using the slope-intercept form of a line: $y = mx + b$ Substituting the slope $m = -1$ and the y-intercept $b = -2$: $y = -x - 2$

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

Would you like further details about this solution or another representation of the equation?

Here are 5 related questions to deepen your understanding:

1. How do you find the equation of a line if two points are not directly visible on the graph?
2. What happens to the equation of a line if its slope is positive instead of negative?
3. How does the y-intercept affect the position of the line on a graph?
4. How can you rewrite $y = -x - 2$ in standard form ($Ax + By = C$)?
5. How do parallel lines differ in their equations?

Tip: Always double-check the points chosen from the graph, as errors in identifying points will lead to incorrect calculations of slope and equation!