Final answer:
The lines passing through the given points are parallel.
Step-by-step explanation:
The given points are (-2,3),(5,-4) and (0,4),(1,3). To determine if the lines passing through these points are parallel, we need to calculate the slopes of the lines. The formula for finding the slope between two points (x1,y1) and (x2,y2) is given by m = (y2 - y1) / (x2 - x1).
For the first pair of points (-2,3) and (5,-4), the slope is m1 = (-4 - 3) / (5 - (-2)) = -7/7 = -1.
For the second pair of points (0,4) and (1,3), the slope is m2 = (3 - 4) / (1 - 0) = -1
Since the slopes of both lines are equal (-1), the lines passing through these points are parallel.