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x y
7 11
8 13
9 15
10 17
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 across all the data points. Let's calculate the ratios for the given data:
For x = 7, y = 11
Ratio = y / x = 11 / 7 = 1.5714
For x = 8, y = 13
Ratio = y / x = 13 / 8 = 1.625
For x = 9, y = 15
Ratio = y / x = 15 / 9 = 1.6667
For x = 10, y = 17
Ratio = y / x = 17 / 10 = 1.7
Since the ratios are not the same for all data points, we can conclude that y does not vary directly with x.
Therefore, there is no constant of variation k, and we cannot write an equation for direct variation between y and x in this case.