Final answer:
The equation to show that y is directly proportional to x, given the constant of proportionality k=12, is y = 12x. When y=24, the value of x that satisfies this equation is x=2.
Step-by-step explanation:
When one variable is directly proportional to another, the relationship between the two can be represented by the equation y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.
In this case, if k=12 and y=24 when x is at a particular value, we can substitute these values into the equation to find that particular value of x. Since k=12, the equation of proportionality becomes y = 12x. To find the value of x when y=24, we simply divide both sides of the equation by 12, giving us x=2.
The value of x when y=24 is shown by y = 12(2), which confirms the original statement that y is directly proportional to x with a proportionality constant of 12.