Write an equation that expresses the following relationship. \[ w \text { varies directly with the square of } u \] In your equation, use \( k \) as the constant of proportionality. \( \square \)

The relationship can be expressed with the equation \( w = k u^2 \), where \( w \) is directly proportional to the square of \( u \), and \( k \) is the constant of proportionality. This means that if you change the value of \( u \), \( w \) will change by the square of that value multiplied by \( k \). This kind of relationship appears frequently in physics, such as calculating gravitational potential energy, which can be represented with a similar quadratic equation involving height. Understanding direct variation helps in graphing relationships, allowing you to visualize how one variable influences another, making it a vital concept in both math and science!