Final answer:
The equation of a line that is parallel to -2x + 6y = 18 is y = -3x + 7.
Step-by-step explanation:
To determine which equation of a line is parallel to the equation -2x + 6y = 18, we need to find the slope of the given equation. The slope-intercept form of a linear equation is y = mx + b, where m is the slope. Rearranging the given equation, we have 6y = 2x + 18, or y = (2/6)x + 3.
Since the slope of this equation is 2/6, any equation with a slope of 2/6 or -2/6 would be parallel to the given equation. The only option that fits this criteria is y = -3x + 7 (option B).