https://r2.erweima.ai/mathbot/image/1726525631520dzh3j97a.jpg

Let's analyze the lines provided in the image:

1. \( y - x = 0 \) can be rewritten as \( y = x \).
2. \( y = 2 \) is a horizontal line where \( y \) is always 2.

To find the intersection point of the two lines, we can substitute \( y = 2 \) into the equation \( y = x \):

\[
x = 2
\]

Thus, the intersection point is \( (2, 2) \).

Now, let's determine in which quadrant the point \( (2, 2) \) lies. Both the x-coordinate and y-coordinate are positive, meaning the point lies in the **first quadrant**.

So the correct answer should be **c. In the first quadrant**, not b.

Would you like more details or have any questions about this?

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Here are five related questions to deepen your understanding:
1. How do you determine which quadrant a point is in?
2. What is the general form of a linear equation?
3. How would the solution change if the lines were parallel?
4. Can two lines intersect in more than one point?
5. How would you find the intersection point of two non-linear curves?

**Tip:** Always check the signs of both coordinates when determining the quadrant of a point.

The two lines y - x = 0 and y = 2 intersect at a point that is located in which quadrant?

Understand how to determine the intersection of two linear equations y = x and y = 2 and identify the quadrant where the point of intersection lies. This problem explains the steps in determining the correct quadrant for a point with positive coordinates. Ideal for students in Grades 6-8.

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