Given a line with the equation \(3x - 4y = 12\). Find the equation of the line that passes through the point (1,2) and is perpendicular to the given line.

Step 1 ：Step 1: Find the slope of the given line by converting the equation to slope-intercept form (y = mx + b). The slope is the coefficient of x. Thus, \(3x - 4y = 12\) becomes \(y = \frac{3}{4}x - 3\). The slope of the given line is \(\frac{3}{4}\).

Step 2 ：Step 2: The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is \(-\frac{4}{3}\).

Step 3 ：Step 3: Use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line. Substitute the slope \(m = -\frac{4}{3}\) and the point (1,2) into the equation, we get \(y - 2 = -\frac{4}{3}(x - 1)\).

Step 4 ：Step 4: Simplify the equation to get it in the form of y = mx + b. After simplifying, the equation is \(y = -\frac{4}{3}x + \frac{10}{3}\).