11. Graph this line using intercepts: $$ 10 x-y=10 $$ Click to select points on the graph.

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UpStudy AI · Accepted Answer

To graph the line $$ 10x - y = 10 $$ using intercepts, follow these steps:

### 1. Find the **x-intercept**
The x-intercept occurs where the line crosses the **x-axis**. At this point, the value of $$ y $$ is **0**.

**Steps:**
- Set $$ y = 0 $$ in the equation.
- Solve for $$ x $$:

$$
10x - 0 = 10 \
10x = 10 \
x = \frac{10}{10} = 1
$$

**x-intercept:** $$ (1, 0) $$

### 2. Find the **y-intercept**
The y-intercept occurs where the line crosses the **y-axis**. At this point, the value of $$ x $$ is **0**.

**Steps:**
- Set $$ x = 0 $$ in the equation.
- Solve for $$ y $$:

$$
10(0) - y = 10 \
0 - y = 10 \
-y = 10 \
y = -10
$$

**y-intercept:** $$ (0, -10) $$

### 3. Plot the Intercepts on a Graph

1. **Plot the x-intercept** at $$ (1, 0) $$.
2. **Plot the y-intercept** at $$ (0, -10) $$.

### 4. Draw the Line

- Use a ruler to draw a straight line passing through both intercept points.
- Extend the line across the graph to visualize the entire line.

### **Graphical Representation**

Here's a simple sketch to illustrate the graph:

```
y
|
10|                     
 |                     
 |                     
 |                     
 |                     
0|----•-------------------•----- x
    1                   0
```

- The **dot at (1, 0)** represents the **x-intercept**.
- The **dot at (0, -10)** represents the **y-intercept**.
- The line connects these two points and extends infinitely in both directions.

### **Summary of Intercepts**
- **x-intercept:** $$ (1, 0) $$
- **y-intercept:** $$ (0, -10) $$

By plotting these two points and drawing a line through them, you have successfully graphed the equation $$ 10x - y = 10 $$ using intercepts.
To graph the line $$ 10x - y = 10 $$, find the x-intercept at $$ (1, 0) $$ and the y-intercept at $$ (0, -10) $$. Plot these points and draw a straight line through them. simplify answer: Plot the points $$ (1, 0) $$ and $$ (0, -10) $$ on the graph and draw a straight line through them to graph the equation $$ 10x - y = 10 $$.

11. Graph this line using intercepts: \[ 10 x-y=10 \] Click to select points on the graph.

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