To graph the equation \( y = -\frac{1}{3}(x - 6) + 2 \), let's break it down and identify key elements:

### 1. **Identify the Slope and y-intercept:**
   - The equation is in point-slope form, \( y = m(x - x_1) + y_1 \).
   - **Slope (m):** \( -\frac{1}{3} \). This means for every unit increase in \( x \), \( y \) decreases by \( \frac{1}{3} \).
   - **Point (x_1, y_1):** \( (6, 2) \) is the point from which the line is drawn.

### 2. **Plot the Point:**
   - Start by plotting the point \( (6, 2) \) on the graph.

### 3. **Use the Slope:**
   - From \( (6, 2) \), move **1 unit to the right** (increase \( x \) by 1) and **1/3 unit down** (decrease \( y \) by \( \frac{1}{3} \)).
   - This gives the next point at \( (7, \frac{5}{3}) \).

### 4. **Draw the Line:**
   - Continue plotting points using the slope, or draw a straight line through the plotted points, extending in both directions.

This graph represents a line with a negative slope, indicating it decreases as \( x \) increases. The y-intercept can be found by setting \( x = 0 \) in the equation, giving \( y = -\frac{1}{3}(-6) + 2 = 4 \).

### Summary:
- **Slope:** \( -\frac{1}{3} \)
- **Point:** \( (6, 2) \)
- **y-intercept:** \( y = 4 \)

Would you like any more details or a visualization?

### Related Questions:
1. How do you find the y-intercept directly from the equation?
2. What is the general form of a linear equation, and how does it differ from the point-slope form?
3. How would you graph a line if the slope were positive instead of negative?
4. How can you determine the x-intercept from this equation?
5. What does the slope of a line indicate about its steepness and direction?

### Tip:
Always remember to check your points by substituting them back into the original equation to ensure accuracy.

Learn how to graph the linear equation y = -1/3(x - 6) + 2 step-by-step. This problem covers key concepts such as point-slope form, slope interpretation, and graph plotting. Suitable for Grades 7-9.

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