Question
For the data in the table, does Y very directly with X, if it does write an equation for the direct variation
Answers
GPT 3.5
To determine if Y varies directly with X, we need to check if the ratio of Y to X remains constant.
Looking at the table:
X | Y
1 | 5
2 | 10
3 | 15
If we divide each Y value by its corresponding X value, we get:
Y/X
5/1 = 5
10/2 = 5
15/3 = 5
As the ratio Y/X remains constant and equal to 5, we can conclude that Y varies directly with X.
To write an equation for direct variation, we can express this relationship as:
Y = kX
Where k represents the constant of variation. As the ratio is 5, k = 5. Therefore, the equation of direct variation is:
Y = 5X
Looking at the table:
X | Y
1 | 5
2 | 10
3 | 15
If we divide each Y value by its corresponding X value, we get:
Y/X
5/1 = 5
10/2 = 5
15/3 = 5
As the ratio Y/X remains constant and equal to 5, we can conclude that Y varies directly with X.
To write an equation for direct variation, we can express this relationship as:
Y = kX
Where k represents the constant of variation. As the ratio is 5, k = 5. Therefore, the equation of direct variation is:
Y = 5X