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

Set \(x = 0\) in the equation \(y=210 - 35x\).
\(y=210-35\times0=210\).
In the context of the situation, when \(x = 0\) (no weeks of purchasing lunches), the amount of money in Amanda's lunch account is \(y = 210\) dollars. So the y - intercept is \((0,210)\).

Step2: Find the x - intercept

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 \(y = 0\) (no money left in the lunch account), \(x = 6\) weeks have passed. So the x - intercept is \((6,0)\).

Answer:

a. The y - intercept is \((0,210)\) (initial amount of money in the account is \(\$210\)). The x - intercept is \((6,0)\) (after \(6\) weeks, the account balance is \(\$0\)).
b. To graph the equation using the intercepts:

• Plot the points \((0,210)\) and \((6,0)\) on the coordinate plane.
• Draw a straight line passing through these two points. This line represents the equation \(y = 210-35x\).