Question

The graph of xy=6 is translated up 3 units and to the right 2 units. Which are possible equations for the translated graph? Select all that apply.

A. y=3+6/x-2
B. y=3x/x-2
C. (x-2)(y-3)=6
D. y=3/x-2

Answer 1

The equation for the graph of xy=6 translated up by 3 units and to the right by 2 units is (x-2)(y-3)=6. This accounts for both the horizontal and vertical translations correctly.

Step-by-step explanation:

The student's question relates to the translation of the graph of the equation xy=6. To find the new equation after the graph is translated up by 3 units and to the right by 2 units, adjustments must be made to the original equation. The horizontal translation to the right by 2 units means substituting x-2 for x, and the vertical translation up by 3 units involves adding 3 to the y value after the equation is solved for y.

The original equation can be rewritten as: y=6/x. To reflect the transformations, you would substitute x-2 for x and then add 3 to the y value: y=3+(6/(x-2)). Therefore, the transformed equation that represents the translated graph is (x-2)(y-3)=6, which can be expanded to (x-2)(y-3)=6.

If we evaluate the provided options, option C, (x-2)(y-3)=6, is the correct equation for the translated graph. Options A, B, and D don't properly reflect both the horizontal and vertical translations as required.