For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
x 4.5, 7.5, 10.5, Y 3, 5, 7,
Yes, y varies directly with x.
To find the equation for the direct variation, we can use the formula y = kx, where k is the constant of variation.
To find k, we can use any pair of values from the table. Let's use the first pair (x=4.5, y=3):
3 = k(4.5)
To solve for k, we divide both sides of the equation by 4.5:
k = 3/4.5 = 0.6667
Now we can write the equation for the direct variation:
y = 0.6667x