Final answer:
The perpendicular slope of the line y = 3x - 2 that passes through the point (2,4) is -1/3.
Step-by-step explanation:
To determine the perpendicular slope of a line, we need to find the negative reciprocal of the given line's slope. The given line is y = 3x - 2, which has a slope of 3. The negative reciprocal of 3 is -1/3, so the perpendicular slope of the line is -1/3.
Let's use the point (2,4) to verify this. We'll find an equation of the line passing through (2,4) with a perpendicular slope of -1/3. Using the point-slope form, the equation will be y - 4 = (-1/3)(x - 2). Simplifying, we get y = -1/3x + 10/3. Therefore, the perpendicular slope of the line y = 3x - 2 that passes through the point (2,4) is -1/3.