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To solve the inequalities using the given graphs of \( y_1 \) and \( y_2 \), let's analyze the intersection and relative positions of the two lines:

- The blue line represents \( y_1 \) and the red line represents \( y_2 \).
- The lines intersect at the point \( (-2, -2) \).

Now, we will solve the three parts based on this information:

### (a) \( y_1 = y_2 \)

This happens at the point where the two lines intersect, which is at \( (-2, -2) \).

**Solution:** \( \{ -2 \} \) in set notation or \( [-2, -2] \) in interval notation.

### (b) \( y_1 > y_2 \)

The blue line (\( y_1 \)) is greater than the red line (\( y_2 \)) to the left of the intersection, i.e., when \( x < -2 \).

**Solution:** \( (-\infty, -2) \)

### (c) \( y_1 \leq y_2 \)

This inequality holds where \( y_1 \) is less than or equal to \( y_2 \), which occurs when \( x \geq -2 \).

**Solution:** \( [-2, \infty) \)

Would you like more details on any of the steps? Here are 5 related questions:

1. How do we find the intersection of two lines algebraically?
2. What methods can be used to solve linear inequalities graphically?
3. How would the solution change if the slope of one of the lines was different?
4. What is the significance of the interval notation used in inequalities?
5. Can you always determine inequalities between lines by looking at their graphs?

**Tip:** When solving inequalities graphically, always pay attention to the intersection points, as they often mark transitions in the inequality signs.

Use the given graphs of y1 and y2 to solve each inequality. Write the solution set in interval notation.

Learn how to solve inequalities graphically using the intersection of two linear equations. Explore the steps to find the solution for y1 = y2, y1 > y2, and y1 ≤ y2, and express the solutions in interval notation. Suitable for high school students studying algebra and coordinate geometry.

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