Draconic Bloodline

The Ur-Dragons fought the Titans and Gods for control of the primeval world, and are the closest to true children of Iroa itself. When the Gods triumphed and swept the Titans aside, the dragons withdrew to the lonely places of the world to seethe and plot. The descendants of the servants to those primal dragons still carry the mark of their ancient masters' power in their blood, and it manifests from time to time, especially in kobolds. Not all draconic sorcerers bear such a lofty lineage, however, and instead are marked by the vast and far-ranging effects that a powerful dragon's lair has upon the surrounding region. You may have first found magic in such a place and so found it turned to this path, or may have even been raised as a dragon's slave.   Draconic Bloodline is a Sorcerer subclass from the PHB. It functions as printed, except as noted below.

Draconic Spells

You know an elemental cantrip of your choice as a bonus cantrip, that must deal damage of your dragon's type. For example, Bonfire, Fire Bolt, and Green Flame Blade would all be suitable for a Red Dragon sorcerer. 
At certain class levels, you add to your spells known from the list below. Unlike the other spells you know, these bonus spells cannot be retrained. This doesn't impede you from retraining spells you learn normally from leveling up as a sorcerer.
1st / Cause Fear, Chromatic Orb
3rd / Alter Self, Dragon's Breath
5th / Fear, Hypnotic Pattern
7th / Polymorph, Secret Chest
9th / Immolation, Legend Lore

Spells Known

You learn spells only from the Sorcerer spell list, but can learn elemental or dragon-themed spells and cantrips from any class's spell list. When you learn an elemental spell or cantrip from a different class list, you must change the element of the spell to the same element as your dragon. For example, Flame Strike would become Cold and Radiant for a White Dragon sorcerer, instead of Fire and Radiant. Note that you are still allowed to learn spells that utilize different elements than you own, just not when using this feature to learn spells from outside your own class list.