Final answer:
The slope of a line parallel to the line 6x - 2y = 1 is 3, because parallel lines have the same slope.
Step-by-step explanation:
To solve the mathematical problem completely and find the slope of a line parallel to the given line 6x - 2y = 1, we first need to convert this equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By rearranging the equation, we get 2y = 6x - 1 and then y = 3x - 0.5.
Thus, the slope of the original line is 3.
Since parallel lines have the same slope, a line parallel to this one will also have a slope of 3.