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To write the equation of the line in slope-intercept form, we need to find the slope \( m \) and the y-intercept \( b \) of the line.

### Step 1: Identify the y-intercept
The y-intercept is where the line crosses the y-axis. From the graph, it crosses at \( (0, 6) \), so:
\[
b = 6
\]

### Step 2: Calculate the Slope
The slope \( m \) is determined by the "rise over run," or the change in y over the change in x between two points on the line.

Using the points \( (0, 6) \) and \( (2, 3) \):
- The change in y (\( \Delta y \)) from 6 to 3 is \( 3 - 6 = -3 \).
- The change in x (\( \Delta x \)) from 0 to 2 is \( 2 - 0 = 2 \).

So the slope \( m \) is:
\[
m = \frac{\Delta y}{\Delta x} = \frac{-3}{2}
\]

### Step 3: Write the Equation
Using the slope-intercept form \( y = mx + b \), we substitute \( m = -\frac{3}{2} \) and \( b = 6 \):
\[
y = -\frac{3}{2}x + 6
\]

### Final Answer
The equation of the line is:
\[
y = -\frac{3}{2}x + 6
\]

Would you like further details or have any questions?

Here are some related questions to explore:
1. How can we find the slope if we know only two points on a line?
2. What is the significance of the y-intercept in a real-world context?
3. How would this equation change if the line had a positive slope?
4. What is the general form of a line's equation, and how does it relate to slope-intercept form?
5. How can we verify if a point lies on this line?

**Tip:** When finding the slope, always use points that are clearly marked on the grid to avoid errors.

Write the equation of this line in slope-intercept form.

Learn how to determine the equation of a line in slope-intercept form by identifying the slope and y-intercept from a graph. This solution includes step-by-step calculations using points on the graph. Suitable for students in Grades 8-10.

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