Final answer:
The slope of a line parallel to the line with equation 6x - y = 1 would be 6. This is because parallel lines share the same slope, and by converting the given equation into y = mx + b form, we determine the slope to be 6.
Step-by-step explanation:
The equation of the line given is 6x - y = 1. To find the slope of this line, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. First, we add y to both sides of the equation, obtaining 6x = y + 1.
Next, we subtract 1 from both sides to get 6x - 1 = y, which can also be written as y = 6x - 1.
From this, we can see the slope (m) is 6. A line parallel to another has the same slope, so the slope of a line parallel to the given one would also be 6.