Throughout this unit, we have learned how algebra can be a method of understanding relationships in ways including linear equations, simultaneous equations, elimination, systems, and so on. All of these parts of algebra connect and relate with each other, for example, simultaneous equations could be solved by elimination, systems could be written through linear equations, etc. Getting on to the big question, we thought of four ways that algebra can help us understand changes in relationships. Firstly, algebra allows us to represent relationships through variables. In general, x and y are used in simple equations, for example, y=x, y=2x. However, as the equation gets complicated, more types of variables are included. Secondly, algebra can be written in equations and inequalities. For instance, y=mx+b, y>x-b, y<mx^2, and following with all other sorts of mathematical expressions. The three equations and inequalities that I wrote represent the relationship between x, y, m, and z (for one time). As an example, the first equation expresses that the y value is the same as the m (slope) multiplied by the x value, and added by the b (y-intercept). Thirdly, algebra can make us understand the relationship through graphing, specifically the rate of change when the value increases or decreases. A linear equation, for example, changes depending on the inserted number of variables. When m increases, the steeper the straight line will be, when b increases the higher the y-intercept will be, and vice versa. Last but not least, algebra is always around us in real-life situations. Some people may think that this is not true, but the world is full of equations. Specifically about the summative task we did, we worked on creating products and considering the product cost, start-up cost, and revenue cost. The product cost (both spending and revenue) represents the x the start-up cost represents the b. Also, the stairs’ steepness could be represented in a graph, where it can be understood that algebraic expressions are right next to us.
Shodai, Jooyong, and Taiga