To find the y-intercept of the line given by the equation \( y = 7x - \frac{12}{7} \), we need to determine the value of \( y \) when \( x \) is equal to 0.
Substituting \( x = 0 \) into the equation:
\[ y = 7(0) - \frac{12}{7} \] \[ y = 0 - \frac{12}{7} \] \[ y = -\frac{12}{7} \]
Therefore, the y-intercept of the line is \(-\frac{12}{7}\).