Answer
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 \( 10x - y = 10 \).
Solution
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.
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