Final answer:
The slope of a line that is perpendicular to a line with an equation of 3x - 2y = 14 is -2/3, as perpendicular slopes are negative reciprocals of each other.
Step-by-step explanation:
The question you have asked pertains to finding the slope of a line that is perpendicular to another given line with the equation 3x - 2y = 14. To determine this, we first need to find the slope of the given equation by rewriting it in slope-intercept form (y = mx + b), where 'm' represents the slope. Manipulating the given equation, we get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of a line that is perpendicular to the one with slope 3/2 is the negative reciprocal of 3/2, which is -2/3.