Question

A gas station sells a coffee mug filled with coffee for $3. For each refill, using the same mug, the gas station charges $1.25 for the coffee. If y represents the total cost and x represents the total number of filled coffee mugs purchased, which function rule describes this pattern?

Answer 1

The function rule that describes this pattern is y = 3 + 1.25x.

Step-by-step explanation:

The function rule that describes this pattern is y = 3 + 1.25x.

Here, y represents the total cost and x represents the total number of filled coffee mugs purchased. The base cost of the coffee mug is $3, so we add this fixed cost to the cost of each refill. Each refill costs $1.25, so we multiply this cost by the number of refills (x) to get the total cost. Therefore, the function rule is y = 3 + 1.25x.

Answer 2

Since the price of the coffee itself is $1.25, the gradient of the function will be 1.25 and will give a straight line. However, since the first cup of coffee costs $3, when extrapolated to x = 0, the price is 3 - 1.25 = $1.75 which indicates the cost of using the cup. Therefore this is the y-intercept. This can be expressed as a linear function of y = mx + c where y is the price, m is the gradient, x is the number of times the cup has been filled with coffee, and c is the price of using the cup, giving:
y = 1.25x + 1.75