Question

Identify the inverse variation equations. Select all that apply.

Y - 1 = 2x
Y - 1 = 2/x
Y = 2x
Y = 2/x
XY = 2

Answer 1

The inverse variation equations from the provided options are Y = 2/x and XY = 2, as they fit the standard form xy = k and depict an inverse relationship between variables x and y.

Step-by-step explanation:

The student's question is asking to identify the inverse variation equations from a given list. In mathematics, inverse variation is when two variables x and y are related in such a way that their product is a constant (k), represented by the equation xy = k. Looking at the options provided, an equation represents an inverse variation if, as one variable increases, the other decreases in such a manner that their product remains the same.

• Y - 1 = 2x is not an inverse variation because it is a linear equation.
• Y - 1 = 2/x resembles an inverse variation, but it needs to be in the standard form xy = k to qualify.
• Y = 2x represents direct variation, not inverse variation.
• Y = 2/x is an inverse variation equation because if you multiply y by x (xy), you get a constant (2).
• XY = 2 is the standard form of an inverse variation equation where the product of x and y is a constant.

Thus, the equations that represent an inverse variation are Y = 2/x and XY = 2.

Answer 2

The inverse variation equations from the options provided are Y = 2/x and XY = 2. These equations show that y varies inversely with x, maintaining a constant product xy.

Step-by-step explanation:

To identify the inverse variation equations from the given options, we need to recognize the form of such equations. An inverse variation is described by the equation y = k/x where k is a constant. This means that as x increases, y decreases proportionally, and vice versa. The product of x and y is constant (xy = k).

Looking at the options given:

• Y - 1 = 2x is not an inverse variation because it describes a linear relationship where y increases as x increases.
• Y - 1 = 2/x resembles an inverse variation, but because it is not in the form y = k/x (it has an extra -1), it is not a true inverse variation equation.
• Y = 2x is a direct variation, where y increases as x increases in a linear fashion.
• Y = 2/x is an example of an inverse variation because y decreases as x increases keeping the product xy constant.
• XY = 2 is also an inverse variation since it can be rearranged to y = 2/x, maintaining a constant product of xy.

Therefore, the equations that represent inverse variations are Y = 2/x and XY = 2.