Given the points (4,4) and ( -2,4) on a line , find the equation of the line.

To find the equation of a line given two points \((4, 4)\) and \((-2, 4)\), we use the point-slope form of the equation of a line. Here's how:

1. **Find the slope \(m\):**

   The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Substituting the given points \((4, 4)\) and \((-2, 4)\):
   \[
   m = \frac{4 - 4}{-2 - 4} = \frac{0}{-6} = 0
   \]

   Since the slope is \(0\), we know that the line is **horizontal**.

2. **Write the equation:**

   For a horizontal line, the equation is of the form:
   \[
   y = c
   \]
   where \(c\) is the constant \(y\)-value for all points on the line.

   Since both points have a \(y\)-coordinate of \(4\), the equation of the line is:
   \[
   y = 4
   \]

### Final Answer:
The equation of the line is \(y = 4\).

Would you like any additional explanation or details?

Here are 5 related questions:
1. What would the equation be for a vertical line?
2. How do you find the equation of a line with a non-zero slope?
3. How do parallel lines relate in terms of slope?
4. Can you find the distance between the two points given?
5. What is the general form of a line's equation?

**Tip**: A horizontal line always has a slope of zero, and its equation is simply \(y = \text{constant}\).

Given the points (4, 4) and (-2, 4) on a line, find the equation of the line.

Learn how to find the equation of a line through points (4, 4) and (-2, 4). This example explains key concepts in algebra and coordinate geometry, including how to calculate the slope of a line and write the equation for a horizontal line. Ideal for students in Grades 6-8.

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