Explanation

If y is directly proportional to x², it means that:

y ∝ x²

This can be written as an equation:

y = kx²

where k is the constant of proportionality.

Given Information:

We are given that y = m for a particular value of x. Let's call this value x₁.

So, we have:

m = kx₁²

Doubling the Value of x:

Now, we double the value of x. Let's call this new value x₂. So, x₂ = 2x₁.

We want to find the new value of y, let's call it y₂, when x = x₂.

Using the proportionality equation:

y₂ = kx₂²

Substitute x₂ = 2x₁:

y₂ = k(2x₁)²

y₂ = 4kx₁²

Substituting the value of kx₁² from the first equation:

We know that kx₁² = m. So, we can substitute this into the equation for y₂:

y₂ = 4m