Linear Functions Applications

Flashcards covering real-world applications of linear functions, including salary calculations, service charges, and rate-based depletion scenarios.

Constant rates of change

The steady rate at which situations follow a predictable pattern, such as savings growing over time or a sports player's training routine building up week by week.

Linear Function Formula

The mathematical equation expressed as $y = mx + b$ or $f(x) = mx + b$.

Carla's Hourly Rate (Example 1)

The amount Carla is paid as a cashier per hour, which is $₱ 60$.

Carla's Weekly Extra Pay (Example 1)

The additional amount Carla receives for working the evening shift, which is $₱ 500$ per week.

Carla's Total Salary Equation (Example 1)

$f(x) = 60x + 500$, where $x$ represents the number of hours worked.

Carla's Week Salary for 32 hours

$₱ 2,420$, calculated using $y = 60(32) + 500$.

Carla's Week Salary for 42 hours

$₱ 3,020$, calculated using $y = 60(42) + 500$.

Carla's Week Salary for 45 hours

$₱ 3,200$, calculated using $y = 60(45) + 500$.

Conference Room Deposit (Example 2)

The fixed charge for using the hotel's conference room, which is $200$ pesos ($b = 200$).

Conference Room Hourly Rate (Example 2)

The cost per hour of use for the conference room, which is $₱ 100$ ($m = 100$).

Conference Room Cost Equation (Example 2)

$y = 100x + 200$, where $x$ is the number of hours and $y$ is the total cost.

Total Cost for 5-hour Room Use (Example 2)

$₱ 700$, calculated using $100(5) + 200$.

Swimming Pool Draining Rate

The rate at which the water is draining from the pool, which is $450012\text{liters per minute}$.

Swimming Pool Maximum Capacity

The amount of water in the pool before draining started, which is $375,000\text{liters}$.

Jeepney Fare Linear Components

The values used to determine the fare where $m = 1.5$ (succeeding kilometer rate) and $b = 7.50$ (first kilometer fare).