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 amanda’s 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 35. this means that after weeks, amanda will have $ in her school lunch account. the ( y )-intercept is 210. this means that there was initially $210 in amanda’s school lunch account.

Explanation:

Step1: Find x - intercept

To find the x - intercept, set \(y = 0\) in the equation \(y=210 - 35x\).
So, \(0=210 - 35x\).
Add \(35x\) to both sides: \(35x = 210\).
Divide both sides by 35: \(x=\frac{210}{35}=6\).
The x - intercept is 6. This means that after 6 weeks, Amanda will have $0 in her school lunch account.

Step2: Find y - intercept

To find the y - intercept, set \(x = 0\) in the equation \(y = 210-35x\).
So, \(y=210-35\times0 = 210\).
The y - intercept is 210. This means that there was initially $210 in Amanda's school lunch account.

Answer:

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