Direct variation :
Two variables x and y show direct variation when
y = ax
for some nonzero constant a.
Another type of variation is called inverse variation.
Inverse variation :
Two variables x and y show inverse variation when they are related as follows:
y = a/x, a ≠ 0
The constant a is the constant of variation, and y is said to vary inversely with x.
Tell whether x and y show direct variation, inverse variation, or neither.
Problem 1 :
xy = 5
Solution :
xy = 5
Solving for x or y, we get
y = 5/x
So, it is inverse variation.
Problem 2 :
y = x − 4
Solution :
y = x - 4
It doesn't have relationship of y = ax or y = a/x. So, it is neither.
So, it is inverse variation.
Problem 3 :
y/2 = x
Solution :
y/2 = x
x = y/2
Multiplying by 2 on both sides.
2x = y
y = 2x
It is direct variation.
Problem 4 :
y = 2/x
Solution :
y = 2/x
It is in the form of y = a/x, here a is constant of variation.
So, it is inverse variation.
Problem 5 :
xy = 12
Solution :
xy = 12
y = 12/x
It is in the form of y = a/x, here a is constant of variation.
So, it is inverse variation.
Problem 6 :
y/x = 8
Solution :
y/x = 8
Multiplying by x on both sides.
y = 8x
It is in the form of y = ax, here a is constant of variation.
So, it is direct variation.
Problem 7 :
4x = y
Solution :
4x = y
y = 4x
It is in the form of y = ax, here a is constant of variation.
So, it is direct variation.
Problem 8 :
x + y = 4
Solution :
x + y = 4
It is not in the form of y = ax or y = a/x. So, it is neither.
Problem 9 :
8y = x
Solution :
8y = x
y = x/8
It is not in the form of y = ax or y = a/x, here a is constant of variation.
So, it is neither.
Problem 10 :
xy = 1/5
Solution :
xy = 1/5
y = 1/5x
It is not in the form of y = ax or y = a/x, here a is constant of variation.
So, it is neither.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM