A line can be expressed in the standard form y = mx + c where m is the slope and c is the y-intercept. For the two line to be parallel they should have the same slope.
Now, y = 7x / 2 - 17/2 has the slope m equal to 7/2
For y = 14x/9 - 24/9 , the slope m is equal to 14/9
Now we see that the slopes of the lines which are 14/9 and 7/2 are not equal. Therefore the two lines are not parallel.
Two lines that are not parallel are intersecting but you do not want the point of intersection, instead you just want to know if they are parallel or not.
Therefore the lines are not parallel.