Both teachers and children are people. If there were 4 teachers and 9 children already at the table, sitting down, when Jim arrived, then that would be 13 people at the table before he sit and 14 people after he sits.
The line y = 12 is a horizontal line with a slope of 0. Therefore a line parallel to line y = 12 will have a slope of 0. A line perpendicular to line y = 12 is a vertical line, the slope of a vertical line is undefined.
