A direct variation includes the points \( (9,18) \) and \( (4, n) \). Find \( n \). Write and solve a direct variation equation to find the answer. \( \quad n= \)

In a direct variation, the relationship between two variables \( x \) and \( y \) can be expressed with the equation \( y = kx \), where \( k \) is a constant. Using the point \( (9, 18) \), we can find \( k \) by substituting: \[ 18 = k \cdot 9 \implies k = \frac{18}{9} = 2 \] Now, using \( k = 2 \), we can find \( n \) using the point \( (4, n) \): \[ n = 2 \cdot 4 = 8 \] Thus, \( n = 8 \). Using the relationship established by direct variation can be handy in various real-life situations, such as physics and economics. For instance, if the distance traveled by an object is directly proportional to the time spent traveling, knowing one of the values allows you to determine the other easily. So, if a car travels 60 miles in 1 hour, it will travel 120 miles in 2 hours using the same ratio!