Determine whether the relation represents \( y \) as a function of \( x \). \[ 8 x+9 y=72 \] This relation is a function because there are values of \( x \) that correspond to more than one value of \( y \) This relation is a function because there is only one value of \( y \) for each input \( x \). This relation is not a function because there are values of \( x \) that correspond to more than one value This relation is not a function because there is only one value of \( y \) for each input \( x \).

To determine whether the relation \( 8x + 9y = 72 \) represents \( y \) as a function of \( x \), we can rearrange the equation to solve for \( y \): \[ 9y = 72 - 8x \] Dividing both sides by 9: \[ y = \frac{72 - 8x}{9} \] From this expression, it’s clear that for each value of \( x \), there is exactly one corresponding value of \( y \). This means that the relation does represent \( y \) as a function of \( x \). So, the correct answer is: This relation is a function because there is only one value of \( y \) for each input \( x \). Let’s dive into some historical tidbits about functions! The idea of functions dates back to the 17th century, notably with mathematicians like René Descartes and Gottfried Wilhelm Leibniz. They laid the groundwork for modern calculus by formalizing the concept of functions and their relationships. For a little real-world application, functions are everywhere! Whenever you're using a formula to calculate your monthly expenses based on your income, you're essentially creating a function. You input your earnings (x) and get your predicted expenses (y) — talk about practical math in action!