They only need to overlap at the start and end, meaning the rest of the line can be way off and it’ll still start and stop at the same places. Here’s a quick graph courtesy of WolframAlpha showing three curves with the same start and end point.
Which line is more gradual or smooth really depends on what you mean by those terms.
Another way to visualise it is to imagine a string tied taut between two posts making a straight line. If you add some slack to the string so it’s no longer taut you’ll see the middle curve as it’s pulled down by gravity, but it’s still tied to the same two posts so it starts and ends in the same place as the taut one.
They only need to overlap at the start and end, meaning the rest of the line can be way off and it’ll still start and stop at the same places. Here’s a quick graph courtesy of WolframAlpha showing three curves with the same start and end point.
Which line is more gradual or smooth really depends on what you mean by those terms.
Another way to visualise it is to imagine a string tied taut between two posts making a straight line. If you add some slack to the string so it’s no longer taut you’ll see the middle curve as it’s pulled down by gravity, but it’s still tied to the same two posts so it starts and ends in the same place as the taut one.