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To determine the equation of the line shown in the graph, follow these steps:

1. **Identify the slope (m):**
   - The slope is the "rise over run," or the change in \( y \) divided by the change in \( x \).
   - From the graph, the line passes through the points \((-3, 3)\) and \((0, 0)\).
   - Slope (\(m\)) = \(\frac{\text{change in } y}{\text{change in } x} = \frac{3 - 0}{-3 - 0} = \frac{3}{-3} = -1\).

2. **Determine the y-intercept (\(b\)):**
   - The \(y\)-intercept is where the line crosses the \(y\)-axis.
   - From the graph, the line crosses the \(y\)-axis at \((0, 0)\). So, \(b = 0\).

3. **Write the equation:**
   - The general slope-intercept form of a line is \(y = mx + b\).
   - Substituting \(m = -1\) and \(b = 0\), the equation of the line is:

   \[
   y = -x
   \]

Let me know if you want additional explanation or assistance! Here are some related questions:

1. What does the slope of \(-1\) represent in real-world scenarios?
2. How can we find the equation of a line if two points are not aligned on a grid?
3. What happens to the graph if the slope changes to a positive value?
4. How do we convert \(y = -x\) into the general form \(Ax + By + C = 0\)?
5. Can we verify the equation using another point from the graph?

**Tip:** Always check the slope by ensuring the points used are accurate to avoid calculation errors!

Find an equation of the line shown in the graph.

Discover how to determine the equation of a straight line from its graph. This problem explains slope calculation and intercept identification, arriving at the equation y = -x. Ideal for Grades 8-10 students learning linear equations.

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