For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
X
Y
4.5
3
7.5
5
10.5
7
Does y vary directly with x?
If yes, 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 constant.
Let's calculate the ratio for each pair of values:
For the first pair (4.5, 3): 3/4.5 = 0.67
For the second pair (7.5, 5): 5/7.5 = 0.67
For the third pair (10.5, 7): 7/10.5 = 0.67
Since the ratio is constant (approximately 0.67), we can conclude that y varies directly with x.
To write an equation for the direct variation, we can use the equation y = kx, where k is the constant of variation. Substituting one of the pairs into the equation, we can solve for k:
3 = 4.5k
k = 3/4.5 = 0.67
The equation for the direct variation is y = 0.67x.