That is correct and they will have different y intercepts
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No. In order to be parallel, two lines would have to have the same slope, and different intercepts.Why? Two lines with different slopes, but the same intercepts would result in two intersecting lines. Two lines with the same slope, and the same intercept would result in the same line. Two lines with the same slope, and different intercepts would be parallel.
No, only lines that have the same slope can be parallel.
The same slope
Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if the product of their slopes is -1. If neither of these conditions are met, the lines are nether parallel, or perpendicular.
The slope of line AB will be 1/2. Two parallel lines will always have the same slope, so if you know the slope of one line that is parallel to another, you know the other line's slope.