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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 ratios of y to x for each pair of values are equal.
First, let's calculate the ratio of y to x for each pair of values:
For the first pair (7, 11), the ratio of y to x is 11/7 = 1.5714.
For the second pair (8, 13), the ratio of y to x is 13/8 = 1.625.
For the third pair (9, 15), the ratio of y to x is 15/9 = 1.6667.
For the fourth pair (10, 17), the ratio of y to x is 17/10 = 1.7.
Since the ratios are not equal for all pairs, y does not vary directly with x. Therefore, we cannot find the constant of variation (k) or write the equation.