The rectangle with vertices $(-1, y), (7, y), (-1, 3)$, and $(7, 3)$ has an area of 72 square units, and $y$ is positive. What is the value of $y$?
The length is the distance between $(-1, 3)$ and $(7, 3)$, which is 8 units. The width is the distance between $(-1, y)$ and $(-1, 3)$, which is $|y - 3|$. So the area is $8 \times |y - 3|$, and I need to solve for $y$ when this is equal to 72. I can divide both sides by 8 to get $|y - 3| = 9$. This means that either $y - 3 = 9$ or $y - 3 = -9$. Solving for $y$, I get $y = 12$ or $y = -6$. But the problem says that $y$ is positive, so I can eliminate $y = -6$. Therefore, the only valid value for $y$ is 12. 