Final answer:
The given equations have slopes of 2 and -2, which are negative reciprocals of each other, so the lines are perpendicular.
Step-by-step explanation:
To determine whether two lines are parallel, perpendicular, coinciding, or only intersecting, we need to compare their slopes. The first equation is already in slope-intercept form (y = mx + b), which reveals a slope of 2. To find the slope of the second equation (6x + 3y = 1), we need to put it into slope-intercept form. By rearranging the equation, we get 3y = -6x + 1, and then by dividing by 3, we find the slope-intercept form as y = -2x + 1/3. The slope here is -2.
Two lines are perpendicular if their slopes are negative reciprocals of each other. Since the slope of the second line is the negative reciprocal of the slope of the first line (m1 = 2 and m2 = -2), the two given lines are indeed perpendicular. Therefore, the correct answer is Option 2: Perpendicular.