The slope of the tangent line that touches the curve $y = 3x^{2} + 7$ at $x = 2$ is $12$.  

1. Verify this is reasonable by sketching the function and drawing a tangent line to the curve at $x = 2$.

2. Use the information above to write the equation of the line tangent to the curve at $x = 2$.

   Hint (b):

   If $x = 2$, then $y = \:?$
   Use the point and the given slope to write the equation of the tangent line.