To find the equation of a line that passes through the given point \((-3, 1)\) with a slope of \(0\), we can again use the point-slope form of the line equation. However, since the slope is \(0\), this line is a horizontal line.

### Understanding the Slope

- A slope of \(0\) means the line is horizontal, and therefore, the value of \(y\) remains constant for all values of \(x\).

### Equation of the Line

For a horizontal line passing through the point \((-3, 1)\), the equation is simply:

\[
y = 1
\]

This means no matter what value \(x\) takes, \(y\) will always be \(1\).

### Summary

The equation of the line that passes through the point \((-3, 1)\) with a slope of \(0\) is:

\[
y = 1
\]

This line is a horizontal line at \(y = 1\).

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What would the line equation be if the slope were \(2\) instead of \(0\)?
2. How do we find the equation of a vertical line passing through a given point, such as \((-3, 1)\)?
3. What are the x-intercepts and y-intercepts of a horizontal line?
4. How would the equation change if the line passed through a different point with a slope of \(0\)?
5. How can we represent a line with an undefined slope?

**Tip:** For horizontal lines, the slope is always \(0\), and the equation takes the form \(y = \text{{constant}}\), where the constant is the y-coordinate of any point the line passes through.

Learn how to find the equation of a horizontal line passing through the point (-3, 1) with a slope of 0. Understand the implications of slope in linear equations. Suitable for Grades 7-9.

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