Question

your coffee store starts each morning with 3600 ounces of their most popular coffee in several pots and only sells 12 ounce cups which is given by the equation 12x + y = 3600. which if the following is the meaning of the y-intercept?

the y-intercept is the amount of coffee you had when you sold 100 cups.

the y-intercept is the amount of time it takes to sell all the coffee.

the y-intercept is the amount of coffee you started with in the morning.

the y-intercept is the number of cups sold when you run out of coffee.

Explanation:

Step1: Recall the definition of y - intercept

The y - intercept of a linear equation \(y = mx + b\) (rewrite \(12x + y=3600\) as \(y=-12x + 3600\)) is the value of \(y\) when \(x = 0\).

Step2: Analyze the meaning of \(x = 0\) in the context

In the equation \(12x + y=3600\), \(x\) represents the number of 12 - ounce cups sold. When \(x = 0\) (no cups sold), \(y=3600\).

Answer:

The y - intercept is the amount of coffee you started with in the morning.