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 x-intercept?

the x-intercept is the amount of time it takes to run out of coffee.
the x-intercept is the number of cups you sold when you ran out popular coffee.
the x-intercept is the amount of coffee you have after 100 cups were sold.
the x-intercept is the amount of coffee you started the morning with.

Explanation:

In the equation \(12x + y=3600\), \(x\) represents the number of cups sold (since each cup is 12 ounces and \(12x\) is part of the total coffee amount). The \(x -\)intercept occurs when \(y = 0\) (no coffee left). When \(y = 0\), we solve \(12x=3600\) for \(x\). This \(x\) value is the number of cups sold when all the coffee (\(y = 0\)) is gone.

• The first option: There is no time variable in the equation \(12x + y = 3600\), so the \(x -\)intercept is not about time.
• The third option: When \(x = 100\), \(y=3600 - 12\times100=2400\) (using the equation \(y = 3600-12x\)), so the \(x -\)intercept is not about the amount of coffee after 100 cups.
• The fourth option: The amount of coffee started with is \(y\) when \(x = 0\) (\(y=3600\)), not the \(x -\)intercept.

Answer:

The \(x -\)intercept is the number of cups you sold when you ran out popular coffee.