Emacs does not have a command backward-kill-line (which would kill the text from the point to the beginning of the line), but it doesn’t really need one anyways. Why so? Simple enough - invoking kill-line with a prefix argument 0 does exactly the same thing!

C-0 C-k
M-0 C-k
C-u 0 C-k

Take your pick! If you’d rather have a quicker way to do backward line killing you might consider rebinding C-Backspace or M-Backspace (both are bound to backward-word-kill by default). Personally I always do word killing with M-Backspace, so I favor rebinding C-Backspace:

(global-set-key (kbd "C-<backspace>") (lambda ()
                                        (kill-line 0)))

This command can be further improved if killing backward factors the current indentation level:

(global-set-key (kbd "C-<backspace>") (lambda ()
                                        (kill-line 0)

Thanks to Steve Purcell for suggesting a similar command in the comments.

The C-Backspace keybinding is available out-of-the-box in Prelude.