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Distinct Lines are two (or more) lines that are not equal. This means that they are not the same line (do not have the same equation)
Undefined slopes belong to lines that are vertical. These lines do not cross the y-axis, but do cross the x-axis. Therefore, the equation for these lines are always: x = # (where # is the value at which the line is crossing the x-axis).
Two parallel lines have equal slopes.
In the standard line equation, y=mx+b, y and x are not constants. They are like the manipulated and responding variables of a science experiment. for two lines to be parallel m must be the same for both lines.
Not enough information has been given but in general the equation of a straight line is y = mx+b whereas m is the slope and b is the y intercept.