To find the equation of the line shown in the graph, we need to determine its slope and y-intercept.

1. Determine the slope (m):

   • From the graph, we can identify two points the line passes through: $(0, -2)$ and $(4, 2)$.
   • The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$
   • Substituting the points $(0, -2)$ and $(4, 2)$: $m = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1$

2. Determine the y-intercept (b):

   • The y-intercept is where the line crosses the y-axis. From the graph, it is clear that the line crosses the y-axis at $(0, -2)$.
   • Therefore, the y-intercept $b$ is $-2$.

3. Write the equation:

   • The slope-intercept form of a line is given by: $y = mx + b$
   • Substituting $m = 1$ and $b = -2$: $y = x - 2$

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

Would you like further details or have any questions?

Here are 5 questions you might want to ask:

1. How do you find the slope of a line using two points?
2. Can you explain how to determine the y-intercept from a graph?
3. What are the different forms of a linear equation?
4. How can you convert the slope-intercept form to the standard form of a line?
5. What are some real-world applications of linear equations?

Tip: When graphing a line, always start by plotting the y-intercept and then use the slope to find other points on the line.