For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
x y
3 5.4
7 12.6
12 21.6
(1 point)
Responses
Not a direct variation
Not a direct variation
Direct variation, y equals 1.8 x.
Direct variation, Image with alt text: y equals 1.8 x.
Direct variation, y equals 4 x.
Direct variation, Image with alt text: y equals 4 x.
Direct variation,y equals five-ninths x.
Not a direct variation
To determine if the data shows a direct variation, we need to see if there is a constant ratio between the values of y and x. Let's calculate the ratios:
For the first row: y/x = 5.4/3 ≈ 1.8
For the second row: y/x = 12.6/7 ≈ 1.8
For the third row: y/x = 21.6/12 ≈ 1.8
Since the ratio y/x is approximately the same for all rows, we can conclude that y varies directly with x.
The equation for direct variation is in the form y = kx, where k is the constant of variation. Here, the constant of variation is 1.8. Therefore, the equation for direct variation is y = 1.8x.