Final answer:
In this problem, we are given that y varies directly with x and we are given the values of y and x at a certain point. We can use the direct variation equation to find the constant of variation and then use that to find the value of x when y is given.
Step-by-step explanation:
Given that y varies directly with x and y = -18 when x = 12, we can use the direct variation equation y = kx, where k is the constant of variation. Plugging in the given values, we have -18 = k(12). So, the value of k is -1.5.
To find x when y = 2, we can use the direct variation equation again. Plugging in the values of y and k, we have 2 = -1.5x. Solving for x, we get x = -4/3 or approximately -1.33.