While Jenny goes on vacation, she puts her two dogs in a kennel. She pays a flat fee of $20 per dog and then pays a certain amount of money each day for each dog. If she leaves the dogs for 5 days, the cost is $540. If she leaves the dogs for 7 days, the cost is $740. Part A Write a linear function to model the relationship between the number of days, x, at the kennel and the total cost, y, for one dog. Part B Explain the meaning of the slope in the context of the problem.

Step-by-step explanation:

let x represent the amount of money that she pays each day for each dog.

Let y represent the total cost for each dog for x days.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (740 - 540)/(7 - 5)

m = 200/2 = 100

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 7, y = 740 and m = 100 into y = mx + c. It becomes

740 = 7 × 100 + c

c = 740 - 700 = 40

The equation becomes

y = 100x + 40

The linear function to model the relationship between the number of days, x, at the kennel and the total cost, y, for one dog is

y = 50x + 20

The slope the rate at which the total cost is changing with respect to the number of days.