Find the $$ x $$-intercept and the $$ y $$-intercept. Then graph the equation. $$ y=-7 $$

Question

UpStudy AI · Accepted Answer

To analyze the equation $$ y = -7 $$, let's determine its intercepts and understand its graphical representation.

### 1. **Finding the Intercepts**

#### **a. X-Intercept**
The **x-intercept** occurs where the graph crosses the x-axis. At this point, the value of $$ y $$ is **0**.

Set $$ y = 0 $$ and solve for $$ x $$:
$$
0 = -7
$$
This equation has **no solution** because $$ -7 $$ does not equal $$ 0 $$.

**Conclusion:**  
There is **no x-intercept** for the equation $$ y = -7 $$.

#### **b. Y-Intercept**
The **y-intercept** occurs where the graph crosses the y-axis. At this point, the value of $$ x $$ is **0**.

Set $$ x = 0 $$ and find $$ y $$:
$$
y = -7
$$
So, when $$ x = 0 $$, $$ y = -7 $$.

**Conclusion:**  
The y-intercept is at the point $$ (0, -7) $$.

### 2. **Graphing the Equation $$ y = -7 $$**

The equation $$ y = -7 $$ represents a **horizontal line** where the value of $$ y $$ is constantly **-7**, regardless of the value of $$ x $$.

#### **Graph Description:**
- **Direction:** Horizontal line.
- **Y-Coordinate:** -7 for all points on the line.
- **X-Intercept:** None (the line never crosses the x-axis).
- **Y-Intercept:** $$ (0, -7) $$.

#### **Graph Illustration:**

Below is a simple representation of the graph:

```
             
y
|
|                            
|                            
|----------------------------- (x-axis)
|                            
|                            
|                            
|                            
|          • (0, -7)
|
|
|
```

- The **dashed line** represents the horizontal line $$ y = -7 $$.
- The **dot** at $$ (0, -7) $$ indicates the y-intercept.

#### **Graph Using Graphing Tools:**

For a more accurate and scaled graph, you can use graphing software or online tools like [Desmos](https://www.desmos.com/calculator) to plot the equation $$ y = -7 $$. Simply enter the equation into the graphing tool, and it will display the horizontal line accordingly.

### 3. **Summary**

- **X-Intercept:** None
- **Y-Intercept:** $$ (0, -7) $$
- **Graph:** A horizontal line crossing the y-axis at $$ (0, -7) $$.

If you have access to graphing paper or digital graphing tools, plotting the point $$ (0, -7) $$ and drawing a horizontal line through it will accurately represent the equation $$ y = -7 $$.
The equation $$ y = -7 $$ is a horizontal line that crosses the y-axis at $$ (0, -7) $$. There is no x-intercept because the line never touches the x-axis.

Find the \( x \)-intercept and the \( y \)-intercept. Then graph the equation. \( y=-7 \)

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions