Final answer:
The direction vector for the line given by x = 2t - 1, y = -3t + 2 is m = (2, -3). Both (4, -6) and (-2, 3) are valid multiples of this direction vector, so 'All of the above' is the correct answer.
Step-by-step explanation:
The given parametric equations for the line x = 2t - 1 and y = -3t + 2 can be used to find the direction vector of the line. The coefficient of t in each equation represents the direction ratio for the respective x and y components. Therefore, the direction vector m can be found by taking the coefficients of t from both equations, which gives us the vector m = (2, -3). Note that the direction vector can be any multiple of this vector.
Option a (m = (4, -6)) is simply twice the vector (2, -3), option b (m = (3/2, -1)) is not a correct multiple, and option c (m = (-2, 3)) is the negative of the vector (2, -3), which signifies the same direction. Thus, both option a and option c are correct direction vectors for the given line, making option d, "All of the above", the correct answer.