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To find the equation of the line shown in the graph, we need to determine its slope and y-intercept.

1. **Determine the slope (m):**
   - From the graph, we can identify two points the line passes through: \((0, -2)\) and \((4, 2)\).
   - The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1}
     \]
   - Substituting the points \((0, -2)\) and \((4, 2)\):
     \[
     m = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1
     \]

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

3. **Write the equation:**
   - The slope-intercept form of a line is given by:
     \[
     y = mx + b
     \]
   - Substituting \( m = 1 \) and \( b = -2 \):
     \[
     y = x - 2
     \]

Thus, the equation that represents the line is:
\[ y = x - 2 \]

Would you like further details or have any questions?

Here are 5 questions you might want to ask:
1. How do you find the slope of a line using two points?
2. Can you explain how to determine the y-intercept from a graph?
3. What are the different forms of a linear equation?
4. How can you convert the slope-intercept form to the standard form of a line?
5. What are some real-world applications of linear equations?

**Tip:** When graphing a line, always start by plotting the y-intercept and then use the slope to find other points on the line.

Learn how to find the equation of a line using two points on a graph with our step-by-step guide. This problem covers key algebraic concepts such as linear equations and slope calculation. Suitable for Grades 7-9.

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