Final answer:
To find the equation of a line perpendicular to 2x - 3y - 4 = 0 that passes through (1, 2), determine the slope of the given line, find the negative reciprocal of it, and use the point-slope form of a linear equation to find the equation of the perpendicular line. The correct answer is option C.
Step-by-step explanation:
To find the equation of a line perpendicular to 2x - 3y - 4 = 0 that passes through (1, 2), we need to determine the slope of the given line and then find the negative reciprocal of it. The given line has the form Ax + By + C = 0, where A = 2, B = -3, and C = -4. The slope of the given line can be found using the formula slope = -A/B. So, the slope of the given line is -2/-3 = 2/3. The negative reciprocal of 2/3 is -3/2.
Now that we have the slope of the desired perpendicular line, we can use the point-slope form of a linear equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values (1, 2) and -3/2, we get y - 2 = -3/2(x - 1). Simplifying this equation gives us 2y - 4 = -3x + 3. Rearranging the terms, we get 3x + 2y - 1 = 0.