Inverse Relationships
I will be showing you an inverse relationship with a graph, table, and equation. Lets say that you are trying to find all of the possible side lengths of a rectangle with an area of 36 inches. Is the data linear or not?
Inverse Graph
This is an inverse graph. I can tell that it is inverse and not linear because it is not a straight line, and it curves the farther it goes down, the more straight it gets toward the end. No mater what, this graph will never hit 0. The reason why it is inverse is because the slope doesn't increase/decrease at a constant rate. This graph has a negative slope. In this particular kind of graph, there is no y-intercept because the line will go on forever without ever touching the x or y axis.
Inverse Table
This is an inverse table. I know that it is inverse because it does not decrease at constant rate and as the length increases, the width decreases, which means that the graph has a negative slope. It doesn't have to have a negative slope to be inverse, but it is common that it does. This means heat the graph will have a negative slope. The other thing that tells you that it is inverse is that if you multiply the x by the y, you get the area or number you were working with. That means hat there is a constant relationship between the independent and the dependent variables, but there isn't a constant rate of change in the data that would make one linear.
Inverse Equation
This is an inverse equation. I know that it is inverse because the y (width) variable times the x (length) variable equals the area. It doesn't have to be multiplication because the equation can be anything within the fact family of Length times width equals 36. So it could be 36/length=width, or 36/width=length, or length times width= 36.
Parent Problem
I had my dad do this problem from the book.It took him about 20 minutes because at first, I had him do the wrong one, oops. He did okay on it so I gave him a B+. The highlighted parts are comments and suggestions, or something he did wrong. He didn't have any questions, and he did better than I thought he would and surprised me again.
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Reflection
I learned a lot about the differences between inverse and linear relationships. I think linear relationships were easier because the inverse were a bit more complicated and it took me a little bit to grasp the concept of it, but I understand now and it's sort of easy to do you just have to understand it. I included this because it's important to know the difference between the two and it's good that I learned the differences.