Final answer:
To find the missing y values for a direct variation, you first calculate the constant of variation using the known x and y values. Once the constant is found, use it to compute y for the given x values. For x=3.5, y=70, and for x=7.5, y=150.
Step-by-step explanation:
If x and y vary directly, it means that when one variable increases, the other also increases proportionally, and when one decreases, the other decreases proportionally. This can be represented by the equation y = kx, where k is a constant.
In order to fill in the missing values for y in the table, we need to find the value of k. We do this by using the pair where both x and y are known.
Let's use x = 0.4 and y = 8 to find the constant k:
8 = k(0.4)
k = 8 / 0.4
k = 20
Now that we know k, we can find the missing value of y when x = 3.5:
y = 20(3.5)
y = 70
For the second missing value, when x = 7.5, we have:
y = 20(7.5)
y = 150
Now, we can fill in the missing values: for x = 3.5, y = 70; and for x = 7.5, y = 150.