Final answer:
The expression that can be used to find the value of y when x is 2 is y = 16. So, the correct option is y / (48) (6) * 2.
Explanation:
Given that y varies directly as x, we can set up a direct variation equation: y = kx, where k is the constant of variation. To find k, we use the given values: when x is 6, y is 48. So, 48 = k * 6. Solving for k gives us k = 8.
Now that we have the value of k, we can use the direct variation equation y = kx to find the value of y when x is 2. Plugging in x = 2 and k = 8, we get y = 8 * 2 = 16.
In a direct variation, the relationship between x and y remains constant, and the constant of variation (k) is the same throughout. Therefore, by finding k using the given values and applying it to the equation, we can determine the value of y when x changes.
Understanding direct variation helps solve problems where one quantity depends on another in a proportional manner. In this case, with y varying directly as x, the constant ratio between y and x helps establish the relationship, allowing us to determine y when x changes to a different value. Hence, the expression y = 16 represents the value of y when x is 2 in the given direct variation scenario.
So, the correct option is y / (48) (6) * 2.