For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
(16,4),(32,16),(48,36)
To determine if y varies directly with x, we can check if the ratio of y to x is constant for all the given data points.
For the first data point (16,4), the ratio of y to x is 4/16 = 1/4.
For the second data point (32,16), the ratio of y to x is 16/32 = 1/2.
For the third data point (48,36), the ratio of y to x is 36/48 = 3/4.
Since the ratio of y to x is not constant for all the data points, y does not vary directly with x. Therefore, we cannot write an equation for direct variation.
To determine whether y varies directly with x, we need to check if the ratio between y and x is always the same for all given data points.
Let's calculate the ratios:
For the first data point (16, 4), the ratio of y to x is 4/16 = 1/4.
For the second data point (32, 16), the ratio of y to x is 16/32 = 1/2.
For the third data point (48, 36), the ratio of y to x is 36/48 = 3/4.
As the ratios are not the same for all data points, y does not vary directly with x.
Therefore, we cannot write an equation for direct variation in this case.
To determine if y varies directly with x, we need to check if the ratio between y and x remains constant for all the data points.
Let's calculate the ratio for the given data points:
For the first data point (16, 4):
Ratio = 4/16 = 1/4
For the second data point (32, 16):
Ratio = 16/32 = 1/2
For the third data point (48, 36):
Ratio = 36/48 = 3/4
Since the ratio between y and x is not constant for all the data points, y does not vary directly with x.
Therefore, we cannot write an equation for direct variation in this case.