Final answer:
None of the provided options are correct for the equation of a line that is parallel to 2y = 4 and passes through the point (2, 2). The correct equation should be y = 2, as it's the horizontal line passing through the given point and parallel to the given line.
Step-by-step explanation:
The question asks for the equation of a line that is parallel to the given line 2y = 4 and passes through the point (2, 2). First, we need to find the slope of the given line by rearranging it into the slope-intercept form, which is y = mx + b, where m represents the slope and b the y-intercept. The given line equation 2y = 4 can be simplified to y = 2, revealing that the line is horizontal with a slope of 0.
Since parallel lines have the same slope, the equation of the line we are looking for must have a slope of 0. The only option with a slope of 0 is an equation where y is equal to a constant. Hence, the correct answer must also be a horizontal line that passes through the y-coordinate of the given point, which is 2.
Option A (y = 2x) and Option D (y = 4x - 2) have non-zero slopes, and Option C (y = 1/2x) also has a non-zero slope. Only Option B (y = 2x + 2) includes the y-value 2, but it incorrectly suggests a positive slope. Therefore, none of the provided options are correct. The correct equation should simply be y = 2, which is a horizontal line passing through the y-coordinate of the given point (2, 2) and is parallel to the line 2y = 4.