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To write an equation in slope-intercept form for the line in the graph, we can follow these steps:

### 1. Identify the Slope (m):
The slope-intercept form of a line is \( y = mx + b \), where:
- \( m \) is the slope
- \( b \) is the y-intercept (where the line crosses the y-axis)

Looking at the graph:
- The line appears to go downwards from left to right, indicating a negative slope.
- Choose two clear points on the line to calculate the slope. Based on the grid:
  - One point is at (0, 3), the y-intercept.
  - Another point is at (3, 0).

Using these two points:
\[
\text{slope } m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1
\]

So, the slope \( m \) is -1.

### 2. Identify the Y-intercept (b):
From the graph, we can see that the line crosses the y-axis at (0, 3). Therefore, the y-intercept \( b \) is 3.

### 3. Write the Equation:
Now that we know the slope \( m = -1 \) and the y-intercept \( b = 3 \), we can write the equation:
\[
y = -x + 3
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -x + 3
\]

Would you like further details, or do you have any questions?

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Here are 5 related questions:
1. How do you determine the slope if the line passes through two different points?
2. How would the equation change if the line had a positive slope?
3. What happens to the equation if the line passes through the origin?
4. How do you convert slope-intercept form to standard form?
5. What does it mean if the slope of a line is zero?

**Tip:** When identifying the slope from a graph, look for two points where the line intersects the grid clearly for accurate slope calculation.

Write an equation in slope-intercept form for the given graph.

Learn how to write a linear equation in slope-intercept form (y = mx + b) from a graph. This problem demonstrates how to identify the slope and y-intercept of a line, using clear steps and examples. Suitable for students in Grades 7-9.

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