https://file.aiquickdraw.com/mathbot/file/1725333290875tjospet8.jpg

The equation in the image is:

\[
ay = 7 - |x|
\]

You also provided the value \( x = 2 \). We can substitute \( x = 2 \) into the equation and solve for \( y \).

### Step-by-Step Solution:

1. **Substitute \( x = 2 \) into the equation:**

\[
ay = 7 - |2|
\]

2. **Calculate the absolute value:**

\[
|2| = 2
\]

So the equation becomes:

\[
ay = 7 - 2
\]

3. **Simplify the equation:**

\[
ay = 5
\]

4. **Solve for \( y \):**

To find \( y \), divide both sides by \( a \):

\[
y = \frac{5}{a}
\]

### Final Answer:
The value of \( y \) is given by:

\[
y = \frac{5}{a}
\]

This is the solution for \( y \) in terms of \( a \).

Would you like more details on this solution, or do you have any other questions?

### Related Questions:
1. What happens to \( y \) if \( a = 1 \)?
2. How does \( y \) change if \( a \) is negative?
3. What is the graph of \( y \) versus \( x \) for this equation when \( a \) is a constant?
4. How would the solution change if \( x = -2 \)?
5. Can you determine the value of \( a \) if \( y = 1 \) when \( x = 2 \)?

### Tip:
When dealing with absolute values in equations, remember that \( |x| \) represents the non-negative value of \( x \). This can change how you approach solving the equation depending on the sign of \( x \).

Learn how to solve the absolute value equation y = 7 - |x| with x = 2. This problem explores concepts of absolute value in equations and provides a step-by-step solution. Suitable for students in Grades 9-12.

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