Question

Kenneth’s Kennel takes care of pets while their owners are on vacation. The table shows the linear relationship between the number of days a pet is kept at the kennel and the total cost.

Kenneth's Kennel
Days Cost
3 $95
4 $120
6 $170
9 $245
10 $270

Which function can be used to find y, the total cost for keeping a pet at the kennel for x days?

Answer 1

The function that represents the linear relationship between the number of days a pet is kept at the kennel (x) and the total cost (y) can be found using the points provided in the table.

First, we can calculate the slope (m) of the line using two points: (3, $95) and (10, $270).

m = (270-95) / (10-3) = 175 / 7 = 25

Next, we can use the slope and one of the points to find the y-intercept (b). Using the point (3, $95):

y = mx + b
95 = 25(3) + b
95 = 75 + b
b = 20

Therefore, the function representing the total cost for keeping a pet at the kennel for x days is:

y = 25x + 20