To identify the equation that represents Michael's second cut, we need to follow a systematic approach:
### Step 1: Understand Parallel Lines
Parallel lines have the same slope. Given that the first cut has the equation:
[tex]\[ y = -\frac{1}{3}x + 6 \][/tex]
The slope of this line is \(-\frac{1}{3}\).
### Step 2: Slope of the Second Cut
Since the second cut needs to be parallel to the first cut, it will have the same slope:
[tex]\[ \text{slope} = -\frac{1}{3} \][/tex]
### Step 3: Use Point-Slope Form
The equation of the second cut should pass through the point \((0, -2)\). The point-slope form of a line's equation is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.
### Step 4: Substitute Known Values
Substitute \(m = -\frac{1}{3}\), \(x_1 = 0\), and \(y_1 = -2\) into the point-slope form equation:
[tex]\[ y - (-2) = -\frac{1}{3}(x - 0) \][/tex]
This simplifies to:
[tex]\[ y + 2 = -\frac{1}{3}x \][/tex]
### Step 5: Solve for \(y\)
To write the equation in slope-intercept form \(y = mx + b\), solve for \(y\):
[tex]\[ y = -\frac{1}{3}x - 2 \][/tex]
### Conclusion
The equation of Michael's second cut is:
[tex]\[ y = -\frac{1}{3}x - 2 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex] [tex]\( \text{iconic} \)[/tex]
