Graph the line that passes through the points left parenthesis, minus, 4, comma, minus, 2, right parenthesis(−4,−2) and left parenthesis, minus, 1, comma, minus, 2, right parenthesis(−1,−2) and determine the equation of the line.


To graph the line passing through the points \((-4, -2)\) and \((-1, -2)\) and determine the equation, follow these steps:

### Step 1: Determine the Slope of the Line
The slope \( m \) of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Substituting the given points \((-4, -2)\) and \((-1, -2)\):

\[
m = \frac{-2 - (-2)}{-1 - (-4)} = \frac{0}{3} = 0
\]

Since the slope is 0, the line is horizontal.

### Step 2: Determine the Equation of the Line
For a horizontal line, the equation has the form:

\[
y = c
\]

Here, \( c \) is the constant \( y \)-value that the line passes through. Since both points have a \( y \)-coordinate of \(-2\), the equation of the line is:

\[
y = -2
\]

### Step 3: Graph the Line
The line \( y = -2 \) is a horizontal line that crosses the \( y \)-axis at \(-2\). To graph this:

1. Plot the points \((-4, -2)\) and \((-1, -2)\) on a coordinate plane.
2. Draw a straight horizontal line through these points.

This line represents the equation \( y = -2 \).

Would you like a visual graph, or do you have any other questions?

### Relative Questions:
1. How do you find the equation of a line with a non-zero slope?
2. What is the significance of the slope in the equation of a line?
3. Can you determine the equation of a vertical line passing through given points?
4. What is the general form of a linear equation?
5. How do you graph a line with a slope different from 0?

### Tip:
For any horizontal line, the slope is always 0, and the equation is simply \( y = \text{{constant}} \).

Graph the line that passes through the points (-4,-2) and (-1,-2) and determine the equation of the line.

Learn how to graph the line that passes through the points (-4, -2) and (-1, -2) and determine the equation of the horizontal line. This problem explores key concepts in algebra and coordinate geometry, including the slope formula and the properties of horizontal lines. Suitable for students in Grades 6-8.

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