Question

1. 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.
b. graph the equation by using the intercepts.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\).
Substitute \(x = 0\) into \(y=210 - 35x\):
\(y=210-35\times0=210\).
In the context, when \(x = 0\) (at the start, 0 weeks of purchasing lunches), Amanda has \(y = 210\) dollars in her lunch account.

Step2: Find the x - intercept

The x - intercept occurs when \(y = 0\).
Set \(y = 0\) in \(y = 210-35x\):
\(0=210 - 35x\).
Solve for \(x\):
\(35x=210\), so \(x=\frac{210}{35}=6\).
In the context, when \(y = 0\) (the account is empty), \(x = 6\) weeks have passed.

Answer:

a. The y - intercept is \((0,210)\) (initial amount in the account) and the x - intercept is \((6,0)\) (number of weeks until the account is empty).
b. To graph using the intercepts:

• Plot the points \((0,210)\) and \((6,0)\) on the coordinate plane.
• Draw a straight line passing through these two points. The line represents the relationship \(y = 210-35x\) where \(x\geq0\) (since weeks can't be negative) and \(y\geq0\) (amount of money can't be negative).