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x y
4 6.4
7 11.2
10 16
13 20.8
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all data points.
Let's calculate the ratios for the given data points:
For (4, 6.4): y/x = 6.4 / 4 = 1.6
For (7, 11.2): y/x = 11.2 / 7 = 1.6
For (10, 16): y/x = 16 / 10 = 1.6
For (13, 20.8): y/x = 20.8 / 13 = 1.6
Since the ratio y/x is constant for all data points (1.6), we can conclude that y varies directly with x.
Now, to find the constant of variation (k), we can choose any data point to calculate it. Let's use the first point (4, 6.4):
k = y/x = 6.4 / 4 = 1.6
Therefore, the constant of variation is k = 1.6.
The equation that represents the direct variation relationship between x and y is:
y = 1.6x