Final Answer:
The slope of the line passing through the points (a,(1)/(a)) and (b,(1)/(b)) is equal to ((1)/(b)) - ((1)/(a)) divided by b - a, which simplifies to (a - b)/(ab).
Step-by-step explanation:
The slope of a line between two points (x₁, y₁) and (x₂, y₂) is calculated using the formula (y₂ - y₁) / (x₂ - x₁). Applying this formula to the given points (a,(1)/(a)) and (b,(1)/(b)), the y-coordinates are (1)/(a) and (1)/(b) respectively, while the x-coordinates are a and b.
Thus, the slope formula for these points becomes ((1)/(b)) - ((1)/(a)) divided by b - a. Simplifying this expression yields (a - b)/(ab) as the slope of the line.
In this scenario, the slope between the points (a,(1)/(a)) and (b,(1)/(b)) is determined by applying the slope formula. By substituting the respective coordinates into the formula and performing the necessary calculations, the expression simplifies to (a - b)/(ab). This final result represents the slope of the line connecting the given points on the Cartesian plane.