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ху
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
y = kx ?
is y always the same multiple of x?
No.
In fact, y = 2x-3
To determine whether y varies directly with x, we need to check if the ratio between y and x remains constant as x is changed.
Let's calculate the ratios for the given values of x and y:
For x = 7, y = 8: 8 / 7 ≈ 1.14
For x = 11, y = 13: 13 / 11 ≈ 1.18
For x = 8, y = 9: 9 / 8 = 1.125
For x = 13, y = 15: 15 / 13 ≈ 1.15
For x = 9, y = 10:10 / 9 ≈ 1.11
For x = 15, y = 17: 17 / 15 ≈ 1.13
Based on these ratios, we can see that they are not constant. Since the ratios are not the same for all values of x and y, this means that y does not vary directly with x.
Therefore, there is no constant of variation (k) and we cannot write an equation for this scenario.