To determine which quadrants contain points on the line given by the equation \( y = \frac{x}{1000} + 1,000,000 \), we will analyze the behavior of the line based on the values of \( x \).
### Step-by-Step Solution:
1. **Identify the equation of the line**:
The equation is given as:
\[
y = \frac{x}{1000} + 1,000,000
\]
2. **Determine the y-intercept**:
When \( x = 0 \):
\[
y = \frac{0}{1000} + 1,000,000 = 1,000,000
\]
This means the line intersects the y-axis at \( (0, 1,000,000) \).
3. **Analyze the slope**:
The slope of the line is \( \frac{1}{1000} \), which is positive. This indicates that as \( x \) increases, \( y \) also increases.
4. **Evaluate for negative \( x \)**:
Let's consider \( x < 0 \):
- If \( x = -1000 \):
\[
y = \frac{-1000}{1000} + 1,000,000 = -1 + 1,000,000 = 999,999
\]
Here, \( y \) is positive.
- If \( x = -1,000,000 \):
\[
y = \frac{-1,000,000}{1000} + 1,000,000 = -1000 + 1,000,000 = 999,000
\]
Again, \( y \) is positive.
5. **Evaluate for positive \( x \)**:
Now consider \( x > 0 \):
- If \( x = 1000 \):
\[
y = \frac{1000}{1000} + 1,000,000 = 1 + 1,000,000 = 1,000,001
\]
Here, \( y \) is positive.
- If \( x = 1,000,000 \):
\[
y = \frac{1,000,000}{1000} + 1,000,000 = 1000 + 1,000,000 = 1,001,000
\]
Again, \( y \) is positive.
6. **Determine the quadrants**:
- For \( x < 0 \) and \( y > 0 \): This is in **Quadrant II**.
- For \( x > 0 \) and \( y > 0 \): This is in **Quadrant I**.
- For \( x < 0 \) and \( y < 0 \): This does not occur based on our evaluations, as \( y \) remains positive for negative \( x \).
7. **Conclusion**:
The line passes through Quadrants I and II. It does not pass through Quadrant III or IV since \( y \) never becomes negative for any value of \( x \).
### Final Answer:
The line \( y = \frac{x}{1000} + 1,000,000 \) contains points in Quadrants I and II.
