Final answer:
After identifying the slopes of the two given lines, it's clear that they are perpendicular to each other because the slopes are inverse reciprocals with opposite signs.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope is the 'b' value in the general form y = a + bx, where 'b' represents the slope.
The first line y = 2x + 6 has a slope of +2. The second line needs to be rearranged to standard form to identify the slope, converting y + 1 = -2x to y = -2x - 1. The slope of the second line is -2.
We know that lines are parallel if they have the same slope and are perpendicular if the product of their slopes is -1. In this case, the two slopes are inverses of each other but with opposite signs, which means the lines are perpendicular. So, the correct answer is (b).