In this episode of Entry to Mathematics, we will attempt to answer the lifelong question -- why do we care about lines?
In reality, and in truth, there are only a few times when we care about lines. Often, they are a simplistic way for us to describe what's happening, and we put a lot of emphasis on them because they are helping us look at other, new ideas such as variables and how they can interact with each other. The intersection of lines also can help us see that in the land of infinite solutions, we often just care about ONE of those solutions.
So, we're going to focus instead on the different FORMS of a line, and why we might use one over the other. If we can connect that to the literal equations, we can see that different forms of the line will give us different information, allowing us to talk about and check on different things. We've introduced a new one -- a parametric. Thus, the location of an object depends on the time. This makes sense at a base level, as it gives bearing to some of the reasons why we care.
Today in class, we will explore some more forms of lines, and try to see if we can come up with better solutions and reasoning for our different ones. The problems we are using are in our folder. Let's do this.