To solve the equation \(6u + w = 2\), we can express it in terms of one variable to see the relationship between \(u\) and \(w\).

### Step-by-Step Solution:

1. **Isolate one of the variables:**

   Let's solve for \(w\) in terms of \(u\):

   \[
   6u + w = 2
   \]

2. **Express \(w\) in terms of \(u\):**

   \[
   w = 2 - 6u
   \]

### Solution:
The relationship between \(u\) and \(w\) is given by:

\[
w = 2 - 6u
\]

This equation shows that for any value of \(u\), you can find the corresponding value of \(w\).

### Example Values:
- If \(u = 0\), then \(w = 2\).
- If \(u = 1\), then \(w = -4\).
- If \(u = -1\), then \(w = 8\).

### Conclusion:
The equation \(6u + w = 2\) represents a line in the \(u-w\) plane, and the above equation \(w = 2 - 6u\) is its slope-intercept form.

Would you like more details or have any questions?

### Related Questions:
1. What is the slope of the line represented by the equation \(6u + w = 2\)?
2. How do you graph the line represented by \(6u + w = 2\)?
3. Can you express \(u\) in terms of \(w\) from the equation \(6u + w = 2\)?
4. What are the intercepts of the line represented by \(6u + w = 2\)?
5. How would you solve the system of equations if there was another equation, such as \(4u - 2w = 5\)?

### Tip:
When isolating variables, always check if the coefficient can be simplified to make calculations easier.

Learn how to solve the linear equation 6u + w = 2 with a step-by-step solution. This problem involves isolating variables and understanding the relationship between u and w. Suitable for students in Grades 7-9.

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