For Week 10 of Math, we had finally moved on from the midterm and we moved on to Relations and Functions. In this unit, we are learning about patterns, graphing and intercepts. We learned about the Cartesian Plane (a graph separated in four quarters) and the four quadrants that make it up. We also learned about coordinates and how we can plot dots on the Cartesian plane and with this information and much more, it helps us to be able to study and predict patterns. For this posts, I will show how you can predict a pattern using a chart and to find the relation between the independent and dependent variables. Before I begin, it is good to look over key terms so that you understand exactly what I mean. As you obviously see above, I mention the key terms Independent and Dependent variables. The Dependent variable is the variable that depends on the Independent variable in a relation. The Dependent variable is also known as the Output or the y variable and in a graph is on the y axis. The Independent variable is what the Dependent variable depends on like how the cost of food (dependent variable) depends on the weight (independent variable). The Independent variable is also known as the Input or the x variable and is found on the x axis of a graph. So now that we got these key words out of the way, we can begin with our example.
For our example, we are going to use a chart showing the relation between the figure number (independent variable) and the number of stars for each figure (dependent variable). In the beginning, we are given the number of stars for the first 3 figures (the next three were not given so I put a squiggly line below to show that I did them after) and it is our job to find the number of stars for the remaining of the chart and to find the relation. So on the right I wrote down the difference in the number of stars between each figure (which is 4) and with that, we automatically know the first part of our relation equation; 4x. Next we need to find the second part of the relation. So what we do is we pick a figure and include the input or the figure number and replace the x to solve the relation. I chose figure 1 and after doing this, I ended up with 4 