Question

1. this question has two parts. first answer part a. then, answer part b.

part a
amanda has $210 in her school lunch account. she spends $35 each week on lunches. the equation y = 210 - 35x represents the total amount in amandas school lunch account y for x weeks of purchasing lunches.

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
the y - intercept is
this means that there was initially $
in amandas school lunch account.

part b
graph the equation by using the intercepts.

Explanation:

Step1: Find the y - intercept

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

Step2: Find the x - intercept

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

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

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

Answer:

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