Bryan bought a box of biscuits for his dog, Anchor. Anchor always gets three biscuits a day. At the start of the tenth day after opening the box, Bryan counts 106 biscuits left in the box. Write an equation to represent the number of biscuits left in the box in slope intercept form of the time, in days. Be sure to define your variables.
Identify the slope and the y-intercept of this function, and explain the meaning of each value in this situation.
Let:
- x be the number of days that have passed since opening the box
- y be the number of biscuits left in the box at this time
Since Anchor always gets three biscuits a day, Bryan uses three biscuits each day. Therefore, the number of biscuits left in the box at any day can be represented as:
y = (106 - 3x)
In this equation, the slope is -3, which represents the rate at which the number of biscuits decrease each day. For every passing day, the number of biscuits left decreases by 3.
The y-intercept is 106, which represents the initial number of biscuits in the box when x = 0 (the start of the tenth day). At the beginning of the tenth day, there were 106 biscuits left in the box.