To determine the slope of the equation \( -2x + 6y = 6 \), we first need to rewrite it in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope.
Starting with the original equation:
\[ -2x + 6y = 6 \]
First, we isolate \( y \):
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Add \( 2x \) to both sides: \[ 6y = 2x + 6 \]
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Divide every term by \( 6 \): \[ y = \frac{2}{6}x + \frac{6}{6} \] \[ y = \frac{1}{3}x + 1 \]
Now, we can see that the slope \( m \) of the equation \( y = \frac{1}{3}x + 1 \) is \( \frac{1}{3} \).
For a line to be parallel to another line, it must have the same slope. Therefore, we are looking for a slope that is equal to \( \frac{1}{3} \).
Among the given options, the slope that is parallel to the original equation is:
1/3.