find the slope of the linear equation, and graph it y=3

To find the slope of the linear equation \(y = 3\), we first need to understand the form of this equation.

### Understanding the Equation

The equation \(y = 3\) represents a **horizontal line** on the Cartesian coordinate plane. For this equation:

- The value of \(y\) is always 3, regardless of the value of \(x\).
- This means that the line is parallel to the x-axis and passes through the point \((x, 3)\) for any value of \(x\).

### Finding the Slope

The **slope** of a line is a measure of how steep the line is. It is calculated as the "rise over run," or the change in \(y\) divided by the change in \(x\) between any two points on the line.

For a horizontal line like \(y = 3\):

- There is no change in the \(y\)-value as \(x\) changes; \(y\) stays constant at 3.
- Therefore, the "rise" (change in \(y\)) is 0.
- The "run" (change in \(x\)) can be any non-zero number, as \(x\) can vary freely.

Since the slope (\(m\)) is calculated as:

\[
m = \frac{\text{change in } y}{\text{change in } x}
\]

For the line \(y = 3\), the change in \(y\) is 0. Thus:

\[
m = \frac{0}{\text{change in } x} = 0
\]

**Slope of the line \(y = 3\) is 0.**

### Graphing the Line

To graph the line \(y = 3\):

1. **Identify the y-intercept**: The line intersects the y-axis at \(y = 3\).
2. **Draw a horizontal line**: Draw a straight line parallel to the x-axis that passes through all points where \(y = 3\).

Here’s a simple sketch to visualize the line:

```
 y
 |
 4 |-----------------
 3 |-----------------  y = 3
 2 |-----------------
 1 |-----------------
   +----------------- 
  0  1   2   3   4   x
```

Would you like more details on this, or do you have any questions?

### Related Questions:

1. What is the slope of the line \(x = 5\)?
2. How would you graph the equation \(y = -2\)?
3. What does a vertical line's slope look like?
4. How can we determine the slope of a line given two points?
5. How does the slope of a line affect its steepness?

**Tip:** A horizontal line always has a slope of 0, and it represents a constant value of \(y\).

Discover how to find the slope of the linear equation y = 3 with a detailed explanation. This problem covers key concepts including linear equations, slope calculation, and Cartesian coordinate plane. Suitable for students in Grades 7-9.

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