Final answer:
After analyzing each pair, it is determined that none of the given pairs of lines are perpendicular to each other, as none of the lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
To determine which pair of lines are perpendicular, it's essential to know that perpendicular lines have slopes that are negative reciprocals of each other. In other words, if one line has a slope of 'm', the line perpendicular to it will have a slope of '-1/m'. Let's analyze each pair:
A: The first line is in slope-intercept form, y = mx + b, with a slope of -4. The second line must be rearranged into slope-intercept form to find its slope. Doing the math, 2y = -8x - 10, then divide by 2: y = -4x - 5. Both lines have the same slope, so they are not perpendicular.
B: The first line, y = 4, is a horizontal line, and the second 'equation', 2 = -2, is not a line but a false statement. Therefore, they cannot be perpendicular: The first equation, after rearrangement, gives y = x - 7, which has a slope of 1. The second equation y = x + 3 also has a slope of 1. Since their slopes are equal, they are not perpendicular; they are parallel.: Each equation represents a horizontal line: y = -8 and y = 2. Since they both have a slope of 0 and are parallel to each other, they are not perpendicular.
So none of the given pairs of lines are perpendicular to each other.