What is the family of curves represented by the equation y = k/x?

What is the family of curves represented by the equation y = k/x?

Step 1: Understand the equation y = k/x. Here, 'k' is a constant that can change.
Step 2: Recognize that this equation describes a relationship between 'x' and 'y' where 'y' decreases as 'x' increases when 'k' is positive.
Step 3: Identify that the shape of the graph for this equation is a hyperbola, which is a type of curve.
Step 4: Note that the value of 'k' affects the position and size of the hyperbola. Different values of 'k' will create different hyperbolas.
Step 5: Understand that the hyperbolas have asymptotes, which are lines that the curves approach but never touch. The asymptotes depend on the value of 'k'.

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