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 2/3 1/2
To determine if the relation in the table represents direct variation, inverse variation, or neither, we can check if the ratio of y to x is constant.
Let's calculate the ratios for each pair:
- For the pair (5, 2):
y/x = 2/5
- For the pair (10, 1):
y/x = 1/10
- For the pair (15, 2/3):
y/x = (2/3) / 15 = 2/45
- For the pair (20, 1/2):
y/x = (1/2) / 20 = 1/40
Since the ratios of y to x are not constant, the relation in the table does not represent direct variation or inverse variation. It is neither.
Therefore, there is no equation that can be written to represent the relation in this case.