Final answer:
To determine the slope of the equation at the point (1,1), take the derivative of the equation with respect to x and solve for dy/dx.
Step-by-step explanation:
The given equation is (x²/⁵ + y²/⁵) = 2. To determine the slope of the equation at the point (1,1), we need to find the derivative of the equation with respect to x.
Taking the derivative of both sides of the equation, we get (2/5)x^(-3/5) + (2/5)y^(-3/5) * dy/dx = 0.
Plugging in the values x = 1 and y = 1 into the equation, we can solve for dy/dx. Simplifying, we find that dy/dx = -1.