What is the relashionship between the lines y=7x+4 and 2y=14x+5?

Parallel, as 2y=14x+5 can be written as y=7x+5/2. As it has the same gradient, it is parallel. It is not perpendicular as perpendicular means at a right angle, which in this case would have a gradient of -1/7
 
A

2y = 14x + 5

can be written as

y = 7x + 5/2

which is the same gradient (i.e. perpendicular) as

y = 7x + 4

They just intercept the y axiz at different points
 
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