South Seminole Middle School wants to make $4,740 from yearbooks. Print yearbooks x cost $60 and digital yearbooks y cost $15. This can be represented by the function 60x + 15y = 4,740. Find the x- and y-intercepts. Interpret the x- and y-intercepts.
x = print yearbooks
y = digital yearbooks
\(\begin{array}{rcll} 60x + 15y &=& 4740 \qquad & | \qquad -60x\\ 15y &=& -60x + 4740 \qquad & | \qquad :15 \\ y & = & -4x +316 \\ \end{array}\)
The line is \( \begin{array}{rcll} \mathbf{y} & \mathbf{=} & \mathbf{-4x +316} \\ \end{array} \)
\(\boxed{~ \text{y-intercept ?} \quad x=0\\ \begin{array}{rcll} \hline y_{\text{intercept}} & = & -4\cdot 0 +316 \\ y_{\text{intercept}} & = & 316 \\ \hline \end{array}\\ 316 \text{ digital yearbooks, no print yearbooks} ~}\)
\(\boxed{~ \text{x-intercept ? } \quad y=0\\ \begin{array}{rcll} \hline 0 & = & -4\cdot x_\text{intercept} +316 \qquad & | \qquad +4\cdot x_\text{intercept}\\ 4\cdot x_\text{intercept} & = & 316 \qquad & | \qquad :4\\ x_\text{intercept} & = & 79\\ \hline \end{array}\\ 79 \text{ print yearbooks, no digital yearbooks} ~}\)
