There are two different kinds of curvy lines in music notation - ties and slurs. Both look very similar on the page, but they do very different things - knowing how to recognize which is which is essential for avoiding confusion when practicing. A slur aplies to two or more different notes and means the different notes should be played legato. You can use slurs for notes in a bar (see example) but you can also use slurs over barlines. A tie is a curved line between two notes from the same pitch that joins their time values together so that they are played as if they were one note. Why not use dotted notes? Because ties are the only way to combine note values across barlines. When you use ties make sure they always start/end on the notehead. Follow me for more!