In Algebra, you often look for what is called the y-intercept, this is where any graph crosses or touches the y-axis. In real-life, this is known as your initial condition.
For example, If you are to purchase membership at a health gym, the registration fee is $50 with a monthly fee of $20. Which of the two costs is you initial condition?
In order to sart your membership, you must pay $50. These $50 are your initial condition because without them, you cannot pay $20 per month. If we were to make a graph of this situation, we would have a starting point at 50 on the y-axis.
Another example, a car rental company rents a car for $55 per day, plus $0.30 per mile driven. Which of the two costs is your initial condition?
In order to rent this car, you would have to pay $55 before you are allowed to drive it. The $55 is the initial condition which is graphed as the starting point on the y-axis.
If you notice on both examples, both have a rate that they are charging. This is the rate of change,or better known as the slope.
As we begin to explore more situtations, you will realize that these situation will fit a linear function.
Assignment:
Identify each initial condition and rate of change in each situation.
1. A large chesse pizzapie costs $9.99 with an additional cost of $0.75 for each additional topping.
2. A person trying to lose weight is currently losing 3 lb per day, this person started losing wieght when he weighed 210 lb.
3. A current elementary school choir has 50 members. Because of video musicals, the choir has been increasing the size of its choir by 2 students per week.
4. At the local gas station, unleaded gas costs $3.40 per gallon. When you drive up to put gas, you already have 2 gallons in your tank.
5. The capacity of the school gym is 2000 students. The students are entering at a rate of 25 students per minute. Currently there are 1255 students in the gym.
6. A blown balloon has a diameter of 8 inches, when blowing air into the balloon, the diameter is growing at a rate of 0.25 inches per second.