To find the slope of the given equation xy = 6, we first need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.
Starting with the equation:
xy = 6
We can isolate y by dividing both sides by x (assuming x ≠ 0):
y = 6/x
This expression can be rewritten as:
y = 6x-1
Now, to find the slope, we can differentiate y with respect to x:
dy/dx = -6x-2
At any given point along the curve, the slope of the line will depend on the value of x. For example, if x = 1, then:
dy/dx = -6(1)-2 = -6
Alternatively, if you were to look for a linear approximation or specific points on the curve, you could substitute different values for x to find corresponding slopes. However, since the original equation does not represent a linear function but rather a hyperbola, the slope will vary depending on the location on the curve.