Graph the equation by plotting points. $$ y=-2 $$ Use the graphing tool on the right to graph the equation. $$ \begin{array}{c} ext { Click to } \ ext { enlarge } \ ext { graph }\end{array} $$

Question

Graph the equation by plotting points. $$ y=-2 $$ Use the graphing tool on the right to graph the equation. $$ \begin{array}{c}	ext { Click to } \ 	ext { enlarge } \ 	ext { graph }\end{array} $$

UpStudy AI · Accepted Answer

To graph the equation $$ y = -2 $$, follow these steps:

### Understanding the Equation
- **Equation:** $$ y = -2 $$
- **Type of Graph:** This is a **horizontal line** where the value of $$ y $$ is always $$-2$$, regardless of the value of $$ x $$.

### Plotting Points
Since $$ y $$ is always $$-2$$, you can choose any value for $$ x $$ and the corresponding $$ y $$ will always be $$-2$$. Here are some points you can plot:

| $$ x $$ | $$ y $$ |
|---------|---------|
| -3      | -2      |
| -2      | -2      |
| -1      | -2      |
| 0       | -2      |
| 1       | -2      |
| 2       | -2      |
| 3       | -2      |

### Steps to Graph
1. **Draw the Coordinate Axes:**
   - Draw a horizontal line for the $$ x $$-axis.
   - Draw a vertical line for the $$ y $$-axis.

2. **Plot the Points:**
   - Mark each of the points from the table above on the graph.

3. **Draw the Line:**
   - Since all points have the same $$ y $$-value, connect them with a straight horizontal line across the graph.

### Visual Representation

Here's a simple ASCII representation of the graph:

```
 y
 |
3|          
2|          
1|          
0|----------•----------•----------•----------
-1|          
-2| • • • • • • • • • • • • • •
-3|          
 |
 +---------------------------------------- x
    -3 -2 -1  0  1  2  3
```

- The horizontal line at $$ y = -2 $$ is represented by the row of dots (•) across the graph.

### Key Features
- **Slope:** The slope of the line is **0** because there is no change in $$ y $$ as $$ x $$ changes.
- **Y-Intercept:** The line crosses the $$ y $$-axis at $$(0, -2)$$.

### Summary
The graph of $$ y = -2 $$ is a straight horizontal line that runs parallel to the $$ x $$-axis and intersects the $$ y $$-axis at $$-2$$. No matter what $$ x $$ value you choose, $$ y $$ will always be $$-2$$.

If you have access to a graphing tool or graph paper, you can plot these points to visualize the line accurately.
To graph the equation $$ y = -2 $$, plot points where $$ y $$ is always $$-2$$ for any $$ x $$ value. Draw a horizontal line across the graph at $$ y = -2 $$.

Graph the equation by plotting points. \( y=-2 \) Use the graphing tool on the right to graph the equation. \( \begin{array}{c}\text { Click to } \\ \text { enlarge } \\ \text { graph }\end{array} \)

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