For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
To determine if y varies directly with x, we need to check if the ratio of y to x is always the same.
From the table, we can see that when x is 1, y is 5. When x is 2, y is 10. When x is 3, y is 15. And when x is 4, y is 20.
To check if the ratio of y to x is always the same, we can divide y by x for each pair of values:
5/1 = 5
10/2 = 5
15/3 = 5
20/4 = 5
Since the ratio of y to x is always 5, we can conclude that y varies directly with x.
The equation for direct variation can be written as:
y = kx
Where k is the constant of variation. In this case, since the ratio of y to x is always 5, the equation for direct variation is:
y = 5x