a In this problem use the algebraic model of an affine plane

a. In this problem use the algebraic model of an affine plane based on Zs i. Find the points on the line 2x 3y 4 ii. What are the equations of the lines that are in the same parallel class as the line i Use the parallel class you described in part ii to determine a Latin square. Exiain iv. 2x +3y 4? how you obtained the Latin square. Now pick a second parallel class and use it to find a Latin square orthogonal to the one you obtained in part iii. For this part give the equations of the lines in the parallel class and the resulting Latin square. v. Verify that the two Latin squares you found are orthogonal

Solution

i) 2x + 3y = 4
Points on the line are (0.5,1), (1,2/3), (-1,2), (-4,4)
ii) The lines parallel to the line 2x + 3y = 4 are 4x + 6y = 8, -2x - 3y = -4 and so on