Question

Explain, in complete sentences, the relationship between the equations of parallel lines.

Answer 1

They have the same slope. If you write the lines in the slope-intercept form, you'll get y=ax+b for each line. A is the slope, b is the y-intercept. For two or more parallel lines the coefficient "a" will be the same.
Hope this helps.

Answer 2

@mathishard13 is correct. The slopes of the two lines must be the same in order for the lines to be parallel. The b part of the equation must be different however, or the lines would be the same exact line.