Example 3 (2004 National College Entrance Examination Hunan Paper) The equation of the line passing through point $P(-1,2)$ and parallel to the tangent line of the curve $y=3 x^{2}-4 x+2$ at point $M$ is $\qquad$ .
Solve: Fill in $2 x-y+4=0$. Reason: According to the problem, $y^{\prime}=6 x-4$. Therefore, the slope of the tangent line at point $M(1,1)$ is $k=\left.y^{\prime}\right|_{x=1}=2$.

Since the required line is parallel to the tangent line of the curve $y=3 x^{2}-4 x+2$ at point $M(1,1)$, the slope of the required line is $k=2$. Because the line passes through point $P(-1,2)$, the equation of the required line is $y-2=2(x+1)$, which is $2 x-y+$ $4=0$.