Multiply the numbers on the major axis which are 2 and -9 to get -18. Subtract from that 3*4 = 12. So -18-12 = -30. That's the determinant.
if you were to use the first ordered pair, your answer would be y - 2 = 11/3(x-7) and with the second ordered pair : y + 9 = 11/3(x-4
