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A line parallel to y = 4x - 2 will have the same slope as the existing line, which is 4. Out of the given options, only C has a slope of 4 (since the coefficient of x is the same). Option A has a different slope of 4 and a different y-intercept of 2, so it is not parallel. Option B has a different slope of 7 and the same y-intercept of 2, so it is also not parallel. Option D has a different slope of 10 and a different y-intercept of -2, so it is not parallel either. Hence, option C is the only equation that represents a line parallel to the given line.