You have the following equations:
9x + 5y = 32
4.5x + 2.5y = 7.5
in order to determine if the lines are parallel or perpedicular, write the previous equations in slope-intercept form y = mx + b, where m is the slope and b the y-intercept:
9x + 5y = 32
5y = -9x + 32
y = -9/5 x + 32/9
y = -1.8 x + 3.5
4.5x + 2.5y = 7.5
2.5y = -4.5x + 7.5
y = -4.5/2.5 x + 7.5/2.5
y = -1.8 x + 3
take into account that two lines are parallel if the slopes of the lines are equal. In this case both lines have slope -1.8.
Hence, the lines are parallel