Select the equation of the line that is perpendicular to y = 9 and passes through the point (5, 2).

To find the equation of a line that is perpendicular to $y = 9$ and passes through the point $(5, 2)$, we can follow these steps:

1. Break Down the Problem

• The line $y = 9$ is a horizontal line, meaning its slope is $0$.
• A line that is perpendicular to a horizontal line must be a vertical line, which has an undefined slope.
• A vertical line can be expressed in the form $x = k$, where $k$ is a constant.

2. Relevant Concepts

• Since the line needs to pass through the point $(5, 2)$, we will use the x-coordinate of this point to find our line's equation.

3. Analysis and Detail

• The x-coordinate of our point is $5$.
• Therefore, the equation of the vertical line that passes through the point $(5, 2)$ is: $x = 5$

4. Verify and Summarize

• The line $x = 5$ is indeed vertical and passes through the point $(5, 2)$, confirming it is perpendicular to the horizontal line $y = 9$.

Final Answer

The equation of the line that is perpendicular to $y = 9$ and passes through the point $(5, 2)$ is: $x = 5$