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The graph you provided shows a straight line with negative slope, crossing the x-axis at a point and the y-axis at another point. We can determine the equation of the line using the slope-intercept form \( y = mx + b \), where:

- \( m \) is the slope of the line.
- \( b \) is the y-intercept (where the line crosses the y-axis).

### Steps to determine the equation:
1. **Identify the y-intercept (b):**
   The line crosses the y-axis at \( y = 4 \), so the y-intercept \( b = 4 \).

2. **Determine the slope (m):**
   Slope \( m \) is calculated as \( \frac{\text{change in } y}{\text{change in } x} \).
   From the graph, one noticeable point is at \( (-4, 0) \), and the y-intercept is \( (0, 4) \). So:
   \[
   m = \frac{4 - 0}{0 - (-4)} = \frac{4}{4} = 1
   \]
   The slope is negative due to the downward direction of the line, so \( m = -1 \).

### Equation:
Now that we have \( m = -1 \) and \( b = 4 \), the equation of the line is:
\[
y = -x + 4
\]

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

Here are 5 related questions you could explore:
1. How can we find the slope of a line using two points?
2. What does the y-intercept tell us about a graph?
3. How would the graph change if the slope were positive?
4. How can we rewrite this equation in standard form \( Ax + By = C \)?
5. What would the equation be if the line passed through the origin?

**Tip:** When graphing a line, always look for clear intercepts on the axes to easily determine the slope and equation.

Learn how to determine the equation of a line from a graph with a slope of -1 and a y-intercept of 4. This problem covers key concepts in coordinate geometry and the slope-intercept form equation. Suitable for students in Grades 7-9.

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