Which of the following lines has no point of intersection with the line `y=-(1)/(3)x + sqrt(2)` ?

Options

A. `y=(1)/(3)x - sqrt(2)`
B. `y=-3x+sqrt(2)`
C. `y=-(1)/(3)x-sqrt(2)`
D. `y=3x-sqrt(2)`

Explanation

To determine which of the given lines has no point of intersection with the line \( y = -\frac{1}{3}x + \sqrt{2} \), we need to identify the slope of the given line and compare it with the slopes of the other lines provided in the options.

### Step-by-step Solution:

1. **Identify the slope of the given line**:
The equation of the line is \( y = -\frac{1}{3}x + \sqrt{2} \). Here, the slope \( m \) is \( -\frac{1}{3} \).

2. **Understand the condition for parallel lines**:
Two lines are parallel if they have the same slope. If two lines are parallel, they will never intersect.

3. **Check the slopes of the other lines**:
We need to check the slopes of the lines provided in the options. We are looking for a line that also has a slope of \( -\frac{1}{3} \).

4. **Identify the line with the same slope**:
Suppose one of the options is \( y = -\frac{1}{3}x + b \) (where \( b \) is any constant). This line has the same slope as the given line, hence it will be parallel and will not intersect.

5. **Conclusion**:
After checking the slopes of all the options, identify which one has the slope \( -\frac{1}{3} \). This line will be the answer as it does not intersect with the given line.

### Final Answer:
The line that has no point of intersection with \( y = -\frac{1}{3}x + \sqrt{2} \) is the one with the same slope, which is \( y = -\frac{1}{3}x + b \) (where \( b \) can be any constant).