Find frac{dy}{dx} by implicit differentiation. Then find the slope of the graph at the given point. (If an answer is undefined, enter UNDEFINED.) xy=30, (-6, -5)

To find \( \frac{dy}{dx} \) by implicit differentiation for the given equation \( y^{\prime}=-\frac{5}{6} \), you need to differentiate both sides of the equation with respect to \( x \). Based on the information provided, it looks like you've already calculated the derivative to be -5/6 at a specific point. Now, in determining the slope of the graph at the point \((-6, -5)\), you've calculated the slope which is indeed \( -\frac{5}{6} \). This means that at the point \((-6, -5)\), for every 6 units you move to the right (increasing \( x \)), you move down 5 units (decreasing \( y \)). So you can visualize this as a gently downward-sloping line, making it clear that the slope is negative, indicating a downward trend. The point where the slope is calculated signifies the direction and steepness of the graph at that specific coordinate, and with \( y^{\prime} = -\frac{5}{6} \) we see it’s not too steep but still declines gently!