Question

Madeline 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. Let CC represent the total cost of using a computer for tt minutes at the internet cafe. A graph of CC is shown below. Write an equation for CC then state the yy-intercept of the graph and determine its interpretation in the context of the problem.

Answer 1

The y-intercept of the function is 4, and in the context of the problem, this represents the initial cost (or the fixed fee) to use the computer at the internet cafe.

To write an equation for the cost function C based on the given graph, we can use the point-slope form of a linear equation:

C = mt + b

where m is the slope and b is the y-intercept.

Let's use the points (0,4) and (5,6) to find the slope m:

`\[ m = \frac{\text{change in } C}{\text{change in } t} = (6-4)/(5-0) = (2)/(5) \]`

Now we can substitute the slope and one of the points into the point-slope form to find b:

`\[ 4 = (2)/(5)(0) + b \]`

b = 4

So, the equation for C is:

`\[ C = (2)/(5)t + 4 \]`

Now, let's determine the y-intercept. The y-intercept occurs when t = 0, so substitute t = 0 into the equation:

`\[ C = (2)/(5)(0) + 4 = 4 \]`

Therefore, the y-intercept of the function is 4, and in the context of the problem, this represents the initial cost (or the fixed fee) to use the computer at the internet cafe.