How would you shift the parent function y = x2 to graph the function y = (x - 4)2 + 5?

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

How can you tell when x and y are not directly proportional?

Which value of m will create a system of parallel lines with no solution? y= mx - 6 8x - 4y = 12