To find the slope of the line parallel to the equation \(-2x + 3y = 6\), we first need to rewrite the equation in the slope-intercept form, \(y = mx + b\), where \(m\) represents the slope.
Starting with the original equation:
\[ -2x + 3y = 6 \]
we can isolate \(y\):
- Add \(2x\) to both sides:
\[ 3y = 2x + 6 \]
- Divide every term by \(3\):
\[ y = \frac{2}{3}x + 2 \]
From the equation \(y = \frac{2}{3}x + 2\), we can see that the slope \(m\) is \(\frac{2}{3}\).
Since parallel lines have identical slopes, a line parallel to this one will also have a slope of \(\frac{2}{3}\).
Now, let's compare this with the options provided:
A. \(\frac{2}{3}\)
B. \(-\frac{3}{2}\)
C. \(-\frac{2}{3}\)
D. \(\frac{3}{2}\)
The only option that has the same slope \(\frac{2}{3}\) is option A.
Therefore, the answer is A. \(\frac{2}{3}\).