To write the equation of this line in slope-intercept form, which is $y = mx + b$, we need to determine two things from the graph:

1. The slope (m): The slope is the change in $y$-coordinates divided by the change in $x$-coordinates (often called "rise over run").
2. The y-intercept (b): This is the point where the line crosses the $y$-axis.

Step 1: Identify the slope

From the graph, I can observe that the line passes through the points $(0, -2)$ and $(3, 1)$.

• The change in $y$ (rise) from $-2$ to $1$ is $1 - (-2) = 3$.
• The change in $x$ (run) from $0$ to $3$ is $3 - 0 = 3$.

Thus, the slope $m = \frac{3}{3} = 1$.

Step 2: Identify the y-intercept

The $y$-intercept is where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $(0, -2)$, so the $y$-intercept $b = -2$.

Final Equation:

The equation of the line in slope-intercept form is:

$y = 1x - 2$

Or simply:

$y = x - 2$

Let me know if you need further clarification, or if you have questions!

Here are 5 related questions to expand on this topic:

1. How do you calculate the slope if you're given two points on a line?
2. What does the slope represent in real-life scenarios?
3. How do you graph a line if you're given an equation in slope-intercept form?
4. What is the significance of the y-intercept in an equation?
5. Can two different lines have the same slope but different y-intercepts?

Tip: Always remember that the slope-intercept form is useful for quickly identifying both the slope and where the line crosses the y-axis.