Question

emily is going to use a computer at an internet cafe. the cafe charges an initial fee to use the computer and then an additional price per minute of usage. an equation representing the total cost of using a computer for t minutes at the internet cafe is given by c = 9 + 0.50t. what is the slope of the equation and what is its interpretation in the context of the problem?

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Identify the slope in the given equation

For the equation \(C = 9+0.50t\), comparing it with \(y = mx + b\) (here \(C\) is like \(y\) and \(t\) is like \(x\)), the coefficient of \(t\) is the slope. So \(m = 0.50\).

Step3: Interpret the slope in the context

In the context of the problem, the slope represents the rate of change of the cost with respect to time. Since the slope \(m = 0.50\), it means that for each additional minute (\(t\) increases by 1) of using the computer, the total cost \(C\) increases by \(0.50\) dollars.

Answer:

The slope of the equation is \(0.50\). It means that the cost of using the computer at the internet cafe increases by \(0.50\) dollars per minute of usage.