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To determine the equation of the line passing through the points \((-3, -1)\) and \((1, -1)\), we can follow these steps:

### 1. Find the slope (\(m\)) of the line:
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, the points are \((-3, -1)\) and \((1, -1)\). Substituting the values:

\[
m = \frac{-1 - (-1)}{1 - (-3)} = \frac{0}{4} = 0
\]

So, the slope \(m = 0\). This means the line is horizontal.

### 2. Write the equation of the line:
Since the slope is 0, the line is horizontal, and the equation of a horizontal line is:

\[
y = \text{constant}
\]

From the points \((-3, -1)\) and \((1, -1)\), we see that the \(y\)-coordinate is \(-1\) for both points. Thus, the equation of the line is:

\[
y = -1
\]

### 3. Graphing the line:
The line passes through the points \((-3, -1)\) and \((1, -1)\) and is horizontal. Therefore, it is a straight line parallel to the x-axis at \(y = -1\).

Would you like a detailed explanation of any part? Let me know if you have further questions.

### 5 Follow-up Questions:
1. What does a horizontal line mean in terms of slope?
2. How do we find the slope if the points were not horizontal?
3. What would the equation look like for a vertical line?
4. How do you calculate the midpoint between two points?
5. Can you find the distance between the two points \((-3, -1)\) and \((1, -1)\)?

### Tip:
When dealing with horizontal lines, the y-value remains constant for all points along the line.

Graph the line that passes through the points (-3, -1) and (1, -1) and determine the equation of the line.

Graph the line that passes through the points (-3, -1) and (1, -1) and determine its equation. This problem demonstrates how to calculate the slope between two points and identify the equation of a horizontal line. Suitable for Grades 7-9.

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