The equation xy = 6 can be rewritten in slope-intercept form (y = mx + b) or by obtaining y’s value in terms of x. To do this, we can rearrange the equation as follows:
1. Start with the equation: xy = 6.
2. To isolate y, divide both sides by x (assuming that x ≠ 0):
y = 6/x.
Now, we need to express this in a form that highlights the slope. The equation y = 6/x can be seen as:
y = 6 * x-1.
This format tells us that the slope is not a constant, but varies with x, as it follows an inverse relationship. The slope, which can be denoted as m, is equal to:
m = -6/x2.
In conclusion, the slope of the line represented by the equation xy = 6 is not constant, but rather varies inversely with the square of the x-value, which means as x increases, the slope decreases, approaching zero, and conversely, as x approaches zero, the slope approaches infinity.