**Write the equation of a line that is *parallel* to \[{y=9}\] and that passes through the point \[{(3,-8)}\].**

To find the equation of a line that is **parallel** to the line \( y = 9 \) and passes through the point \( (3, -8) \), follow these steps:

### 1. Identify the slope of the given line:
The equation \( y = 9 \) is a horizontal line. The slope (\( m \)) of a horizontal line is 0.

### 2. Determine the slope of the parallel line:
Since parallel lines have the same slope, the line we are looking for will also have a slope of \( m = 0 \).

### 3. Write the equation of the line:
A line with a slope of 0 is also a horizontal line. The equation of a horizontal line is of the form \( y = \text{constant} \).

Since the line must pass through the point \( (3, -8) \), the constant will be the \( y \)-coordinate of this point. Therefore, the equation of the line is:
\[
\boxed{y = -8}
\]

This is the equation of the line that is parallel to \( y = 9 \) and passes through the point \( (3, -8) \).

Would you like more details on any part of this solution? Here are some related questions:

1. How do you find the equation of a line perpendicular to a horizontal line?
2. What would the equation be if the line were vertical instead of horizontal?
3. How do you graph horizontal and vertical lines?
4. What is the general form of the equation of a line parallel to a given horizontal line?
5. How can you find the distance between two parallel lines?

**Tip:** Horizontal lines always have the form \( y = \text{constant} \), and their slope is 0.

Learn how to find the equation of a line that is parallel to y = 9 and passes through the point (3, -8). This problem involves understanding the concept of parallel lines and how to determine the equation of a line given its slope and a point it passes through. Suitable for students in Grades 9-10.

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