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 :
Solution :
Finding the product of x and y :
x = 2 y = -12 xy = -24 |
x = 4 y = -6 xy = -24 |
x = 6 y = -4 xy = -24 |
x = 8 y = -3 xy = -24 |
The product of x and y is constant.
Finding the ratio of y t ox :
x = 2 y = -12 y/x = -6 |
x = 4 y = -6 y/x = -3/2 |
x = 6 y = -4 y/x = -2/3 |
x = 8 y = -3 xy = -3/8 |
The ratio is not a constant. So, the given table represents the direct variation.
Problem 2 :
Solution :
Finding the product of x and y :
x = 1 y = 2 xy = 2 |
x = 2 y = 4 xy = 8 |
x = 3 y = 8 xy = 24 |
x = 4 y = 16 xy = 64 |
The product of x and y is not constant.
Finding the ratio of y t ox :
x = 1 y = 2 y/x = 2 |
x = 2 y = 4 y/x = 2 |
x = 3 y = 8 y/x = 8/3 |
x = 4 y = 16 y/x = 4 |
The ratio of y to x is not constant. So, the table represents the neither relationship.
Problem 3 :
Solution :
Finding the product of x and y :
x = -4 y = 20 xy = -80 |
x = -3 y = 15 y/x = -45 |
x = -2 y = 10 y/x = -20 |
x = -1 y = 5 y/x = -5 |
The product of x and y is not a constant.
Finding the ratio of y to x :
x = -4 y = 20 y/x = -5 |
x = -3 y = 15 y/x = -5 |
x = -2 y = 10 y/x = -5 |
x = -1 y = 5 y/x = -5 |
The ratio between y to x is constant. So, the table represents inverse variation.
Problem 4 :
Solution :
Finding the product of x and y :
x = 1 y = 60 xy = 60 |
x = 2 y = 30 xy = 60 |
x = 3 y = 20 xy = 60 |
x = 4 y = 15 xy = 60 |
The product of x and y is constant.
Finding the ratio between y to x :
x = 1 y = 60 y/x = 60 |
x = 2 y = 30 y/x = 15 |
x = 3 y = 20 y/x = 20/3 |
x = 4 y = 15 y/x = 15/4 |
The ratio between y to x is not constant. So, it is direct variation.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM