Find the equation of the line parallel to the line $y=3x+2$ and passing through the point $(4,-2)$

Step 1 ：Step 1: The slope of the given line is 3, and parallel lines have the same slope. So, the slope of the line we are looking for is also 3.

Step 2 ：Step 2: Now we use the point-slope form of a line, which is $y-y_1=m(x-x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. In this case, $m=3$ and $(x_1,y_1)=(4,-2)$, so we substitute these values into the equation to get $y-(-2)=3(x-4)$.

Step 3 ：Step 3: Simplify this equation to get the standard form of the line. First simplify the left side to get $y+2=3(x-4)$, then distribute the 3 on the right side to get $y+2=3x-12$, and finally subtract 2 from both sides to get $y=3x-14$.