The slope of a line parallel to another line are equal, and the slope of a line and a perpendicualr line is the reciprocal. So, a line parallel to y = -1/2x + 6 that goes through (4,10) will have an equation of y = -1/2x + 10 (slope is the same and y-intercept changed). The line perpendicular would have an equation that looks like this: y = 2x + 10 (the slope is the reciprocal of the original slope).