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 \(y = 3x - 14\).