Linear algebra

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The linear equation is the most basic type of equation that you’ll deal with in Algebra 1, but it also happens to be one of the most useful. There are a whole lot of scenarios that can be modeled with a linear equation, and they all require two things:

  • Requirement #1: You start at some fixed value that doesn’t change. This could be the starting funds for a business, how high a ball starts over the ground, or how many apples are in a bucket. This amount is represented by the y-intercept.
  • Requirement #2: Whatever the fixed value above measures changes at a constant rate. This amount is represented by the slope.

A basic example would be if you started with $100 in a bank account and added $10 to it each month. In this example, your y-intercept would be $100 since that is your starting value, and your slope would be $10 since that’s how much your account balance is changing over each measure of time. Note that the x-axis would be measured in months.

Linear algebra

Here’s another example. Suppose we start with a bucket that has two pints of water in it, and every time a car goes past, we put a half-pint of water in the bucket. The y-intercept is 2, since that’s how many pints we start with. The x-axis will be measured in how many cars go by since that is what is driving our change in the amount of water in the bucket. Along similar lines as our previous example, the slope will be 1/2 since that’s how much the amount of water in the bucket is changing each time.

For a third example, suppose you have $500 in a savings account, and spend $25 of it each time you go to your favorite store. The y-intercept is 500 since that is the starting amount, and the slope is -25 since that’s the change each time you go to the store. The number of times you go to the store is what is driving the change in the amount of money in the savings account, so the x-axis will be based on how many times you have gone to that particular store.