Find the equation of the line that is perpendicular to the line \(3x - 2y = 5\) and passes through the point \((1, 2)\).

Step 1 ：1. The first step is to find the slope of the given line. In general, if a line's equation is in the form \(Ax + By = C\), its slope is \(-\frac{A}{B}\. In this case, the given line's equation is \(3x - 2y = 5\), so its slope is \(-\frac{3}{-2} = 1.5\).

Step 2 ：2. The slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope. Therefore, the slope of the line we are trying to find is \(-\frac{1}{1.5} = -\frac{2}{3}\).

Step 3 ：3. Using the point-slope form of a linear equation (\(y - y1 = m(x - x1)\)), where \(m\) is the slope and \((x1, y1)\) is a point on the line, we can plug in the slope we found and the given point \((1, 2)\) to find the equation of the line. This gives us \(y - 2 = -\frac{2}{3}(x - 1)\).

Step 4 ：4. Simplifying this equation gives \(y = -\frac{2}{3}x + \frac{4}{3} + 2\), or \(y = -\frac{2}{3}x + \frac{10}{3}\).