Yes, any two parallel lines have the same slope.
For example, graphing out y = 2x+5 and y = 2x+7 will produce parallel lines (both lines have a slope of 2). The two lines will never cross. Algebraically we can solve this system of equations as follows:
y = 2x+5 ... start with the first equation
2x+7 = 2x+5 ... replace y with 2x+7
2x+7-2x = 2x+5-2x .... subtract 2x from both sides
2x-2x+7 = 2x-2x+5
0x+7 = 0x+5
0+7 = 0+5
7 = 5 ... we have a contradiction and false statement here
Because of the false equation in the last line, the original system mentioned above does not have any solutions. A solution to a system is one where the two lines cross.
