To find the equation of the line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we can observe the line in the graph for two main details:

1. Y-Intercept ($b$): This is the point where the line crosses the y-axis.
2. Slope ($m$): The slope is calculated by the rise (change in $y$) over the run (change in $x$) between two points on the line.

Step 1: Identify the Y-Intercept

From the graph, the line crosses the y-axis at $y = 3$. Therefore, the y-intercept, $b$, is 3.

Step 2: Calculate the Slope

To calculate the slope, we select two points on the line:

• One point is $(-9, 0)$.
• Another point is $(0, 3)$.

Using these points: $m = \frac{\text{rise}}{\text{run}} = \frac{3 - 0}{0 - (-9)} = \frac{3}{9} = \frac{1}{3}$

Step 3: Write the Equation

Substituting $m = \frac{1}{3}$ and $b = 3$ into the slope-intercept form, the equation of the line is: $y = \frac{1}{3}x + 3$

Would you like more details or have any questions?

Here are some related questions to expand on this topic:

1. How do you determine the slope if the points are not clearly on grid lines?
2. What are alternative forms to write the equation of a line, and how do they compare?
3. How would the equation change if the line had a negative slope?
4. How do you convert the equation from slope-intercept form to standard form?
5. What happens to the equation if the y-intercept changes?

Tip: The y-intercept is always where $x = 0$; this is a quick way to locate it on any graph.