Question

The manager of a restaurant found that the cost to produce 150 cups of coffee is ​$ 20.00​, while the cost to produce 400 cups is ​$ 45.00. Assume the relationship between the cost y to produce x cups of coffee is linear. Write a linear equation that expresses the​ cost, y, in terms of the number of cups of​ coffee, x.

Answer 1

Answer: Our required linear equation would be
`10y-x=50`

Explanation:

Since we have given that

Number of cups = 150

Cost = $20

Number of cups = 400

Cost = $45

Let x be the number of cups, y be the cost .

We will use "Equation of line using Two point slope":

`y-20=(45-20)/(400-150)(x-150)\\\\y-20=(25)/(250)(x-150)\\\\10(y-20)=(x-150)\\\\10y-200=x-150\\\\10y-x=-150+200\\\\10y-x=50`

Hence, our required linear equation would be
`10y-x=50`