Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table
To determine whether the data represents a direct variation or an inverse variation, we need to check if there is a constant ratio between the two variables.
Table:
x | y
1 | 9
2 | 4.5
3 | 3 \(\frac{9}{3} = 3\)
Since the ratio between y and x is constant (3 in this case), the data represents a direct variation.
Now, let's find the equation to model the data.
The equation of direct variation is given by the formula: y = kx, where k is the constant of variation.
To find the value of k, we can pick any of the data points. Let's choose (1, 9):
9 = k(1)
Solving for k, we find k = 9.
Therefore, the equation to model the data in the table is:
y = 9x