Find all the equations of the straight lines in the family of the lines y=mx-3, for which m and the x - coordinate of the point of intersection of the lines with x-y=6 are integers.

Find atleast two equations of the straight lines in the family of the lines y=5x+b, for which b and the x-coordinate of the point of intersection of the lines with 3x-4y=6 are integers.

Find the equations of the straight lines in the family of the lines y = mx +2 , for which m and the x - coordinate of the point of intersection of the lines with 2x + 3y = 10 are integers.

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a)2 (b) 0 (c) 4 (d) 1

Find the equations of two straight lines which are parallel to the line 12x+5y+2=0 and at a unit distance from the point (1, -1).