Parallel lines are straight lines that never meet. Therefore, they must have identical slopes and different y-intercepts. for the equation y=mx+b, we are given m (the slope) = -1/2 and a coordinate (-4,2) which is (x,y). Now just plug the numbers in 2 = (-1/2)(-4)+b. With this, you can find that b = 0 and so the final equation for the parallel line is y=-1/2x
Perpendicular lines are lines that intersect at a 90 degree angle. Therefore, their slopes are the opposite sign and the reciprocal. The opposite reciprocal of -1/2 is 2. Then you just repeat the same process above to find the equation. m=2, x=-4, and y=2, so plugging in you would get 2 = (2)(-4)+b. Simplifying you get b=10 and so your equation for the perpendicular line that passes through (-4,2) is y=2x+10