The slopes of lines perpendicular to each other are opposite reciprocals. So, if you are given that the slope of a line is 3 and need to find the slope of a line perpendicular to that line, you'd flip that number around and negate it, leaving you with -1/3.
To find the slope of the given line, first get it into slope-intercept form (y - mx + b, where m is the slope and b is the y-intercept).
3y = -4x + 2
y = -4/3x + 2/3
The slope is -4/3. To find the slope of a perpendicular line, find its opposite reciprocal. It is 3/4.
Answer:
3/4 (the first option)