Which of the following represent inverse variation? Select all that apply.
(2 points)
Responses
y=4x
y=−7x
x=9y
y=x8
xy=12
The equations that represent inverse variation are:
1) y=4x
2) y=−7x
3) x=9y
4) xy=12
So, all of the given equations represent inverse variation.
x y = 12
is
y = 12 / x
which is an inverse relationship.
Apologies for the mistake. Yes, you are correct. The equation "xy=12" represents inverse variation because it can be written as "y = 12/x". Thank you for pointing that out.
Inverse variation is a type of relationship between two variables where their product is constant. To determine which of the following equations represent inverse variation, we need to check if the equations can be written in the form y = k/x, where k is a constant.
Let's analyze each equation:
1. y = 4x: This equation is not in the form y = k/x, so it does not represent inverse variation.
2. y = -7x: This equation is not in the form y = k/x, so it does not represent inverse variation.
3. x = 9y: This equation can be rearranged to y = 1/9x, which is in the form y = k/x. Therefore, this equation represents inverse variation.
4. y = x^8: This equation is not in the form y = k/x, so it does not represent inverse variation.
5. xy = 12: This equation can be rearranged to y = 12/x, which is in the form y = k/x. Therefore, this equation represents inverse variation.
From the analysis above, equations 3 (x = 9y) and 5 (xy = 12) represent inverse variation.