Question

this question has two parts. first, answer part a. then, answer part b.
part a
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 purchasing lunches.
a. find the x - and y - intercepts and interpret their meaning in the context of the situation.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\).
Substitute \(x = 0\) into the equation \(y=210 - 35x\).
\(y=210-35\times0=210\).
In the context of the situation, when \(x = 0\) (i.e., at the start, before any weeks of purchasing lunches), the amount of money in Amanda's school lunch account is \(y = 210\) dollars.

Step2: Find the x - intercept

The x - intercept occurs when \(y = 0\).
Set \(y = 0\) in the equation \(y = 210-35x\).
\(0=210 - 35x\).
Add \(35x\) to both sides: \(35x=210\).
Divide both sides by \(35\): \(x=\frac{210}{35}=6\).
In the context of the situation, when \(y = 0\) (i.e., when the money in the lunch account is exhausted), \(x = 6\) weeks have passed.

Answer:

The y - intercept is \((0,210)\), which means Amanda has $210 in her lunch account at the start (before any weeks of buying lunches). The x - intercept is \((6,0)\), which means after 6 weeks of spending $35 per week on school lunches, the money in her lunch account is used up.