Question

school lunch amanda has $210 in her school lunch account. she spends $35 each week on school lunches. the equation y = 210 - 35x represents the total amount in amandas school lunch account y for x weeks of buying lunches. a. find the x - and y - intercepts and interpret their meaning in the context of the situation. the x - intercept is this means that after weeks, amanda will have $ in her school lunch account. the y - intercept is this means that there was initially $ in amandas school lunch account.

Explanation:

Step1: Find the y - intercept

The equation of the line is $y = 210-35x$. The y - intercept is the value of y when $x = 0$. Substitute $x = 0$ into the equation: $y=210 - 35\times0=210$. This means that initially, there was $210$ in Amanda's school lunch account.

Step2: Find the x - intercept

The x - intercept is the value of x when $y = 0$. Set $y = 0$ in the equation $0=210 - 35x$. Then, solve for x:
\[

$$\begin{align*} 35x&=210\\ x&=\frac{210}{35}=6 \end{align*}$$

\]
This means that after 6 weeks, Amanda will have $0$ in her school lunch account.

Answer:

The y - intercept is 210. This means that there was initially $210$ in Amanda's school lunch account.
The x - intercept is 6. This means that after 6 weeks, Amanda will have $0$ in her school lunch account.