Essay
Note: Your teacher will review your response to ensure you receive proper credit for your answer.
Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.
x 5 10 15 20
y 2 1 StartFraction 2 over 3 EndFraction StartFraction 1 over 2 EndFraction
To determine if the relation in the table represents direct variation, inverse variation, or neither, we need to check if the ratio of y to x remains constant.
Let's calculate the ratio of y to x for each pair of values:
For x = 5, y = 2, the ratio y/x = 2/5 = 0.4
For x = 10, y = 1, the ratio y/x = 1/10 = 0.1
For x = 15, y = 2 2/3, the ratio y/x = 8/15 = 0.533
For x = 20, y = 1/2, the ratio y/x = 1/40 = 0.025
Since the ratios of y to x are not constant, the relation in the table does not represent direct variation.
To determine if the relation represents inverse variation, we need to check if the product of x and y remains constant. Let's calculate the product of x and y for each pair of values:
For x = 5, y = 2, the product x*y = 5*2 = 10
For x = 10, y = 1, the product x*y = 10*1 = 10
For x = 15, y = 2 2/3, the product x*y = 15*(8/3) = 40
For x = 20, y = 1/2, the product x*y = 20*(1/2) = 10
Since the product of x and y is not constant, the relation in the table does not represent inverse variation either.
Therefore, the relation in the table represents neither direct variation nor inverse variation.
Equation for the relation: Since the relation does not follow direct or inverse variation, we cannot write a simple equation to represent the relationship between x and y. The relationship between x and y in this case is more complex and cannot be represented by a single equation.