Does the relationship between x and y shown in the table represent a direct variation, an inverse variation, or neither?
x: 2 4 10 13
y: 13 23 53 68
To determine if the relationship between x and y represents a direct variation, an inverse variation, or neither, we can compare the ratios of y/x for each pair of values.
For x=2, y=13: 13/2 = 6.5
For x=4, y=23: 23/4 = 5.75
For x=10, y=53: 53/10 = 5.3
For x=13, y=68: 68/13 ≈ 5.23
Since the ratios of y/x are not constant, the relationship between x and y does not represent a direct variation.
To determine if it represents an inverse variation, we can check the ratios of x*y:
For x=2, y=13: 2*13 = 26
For x=4, y=23: 4*23 = 92
For x=10, y=53: 10*53 = 530
For x=13, y=68: 13*68 = 884
Since the ratios of x*y are not constant, the relationship between x and y does not represent an inverse variation either.
Therefore, the relationship between x and y shown in the table represents neither a direct variation nor an inverse variation.