You can identify parallel lines by the fact that they are the same gradient.
y = 3x + 1 and y = 3x - 7 are parallel. They both have a gradient of 3.
y = 3x + 1 and y = 7 - 3x are not parallel. The first has a gradient of 3, whereas the second has a gradient of - 3.
You need to make sure that the equation of the line is in the form y = mx + c as this is the only way of finding what the gradient is. If the line has a different form, rearrange to y = mx + c. m represents the gradient of the line.
Two lines have the equations y = 5x + 2 and 2y + 6 = 10x. Are these two lines parallel?
y = 5x + 2 is already in the correct form, so it can stay as it is. The gradient of this line is 5.
2y + 6 = 10x is not in the correct form, so we need to rearrange.
2y = 10x - 6
y = 5x - 3
The gradient of the second line is 5.
The gradients of both lines are 5, so yes, they are parallel.