Purpose

I was tasked with creating my own Linear System. I was told to write out two equations, graph them, then solve them algebraically as shown in my image below.

Curricular Response

I chose the first line because I wanted a simple equation, most of our equations now are very complex and I wanted to scale it down. I chose the second equation because I felt it would be informative and interesting to use a Zero slope or, a horizontal line. My strategy was to create the second line first then pick a “good point” along that line to start my line, I then randomly picked a “simple” slope and followed it until it met the y-axis where I then wrote the y-int in my equation. I chose y-int’s of 7 for the first equation and 1 for the second. I chose a slope of 3 or 3/1 for the first equation and a slope of 0 (zero slope) for the second. For my method of solving I chose substitution because it made the most sense, and was the quickest because I already had a variable in one equation isolated, in this case it was the “y” from y=1. I then replaced “y” in the first equation with “1”. Once I simplified the equation and got it to “x=”, I took that x value and plugged it in to my second equation however, in my case there was no x value in my second equation and it already was simplified to “y=”. the solution of the Linear System or, where the two lines meet on the graph is, (-2,1) or x=-2, y=1.

Core Competency Self-Assessment

-I can understand and share information about a topic in a clear, organized way by showing in multiple forms what I’ve learnt. I wrote out equations I created myself, I then illustrated I can graph these lines, and then I showed I can solve these systems algebraically.
-I can show a sense of accomplishment and joy. I take pride in my work and myself, I took my time to make neat lines, I took my time to write well crafted sentences, this shows I take pride in my work, and that I feel accomplished and proud of what I’ve created.
-I can persevere over time to develop my ideas, and I expect setbacks and failure, but use that to develop my ideas. I had a small failure when I tried to get my two lines to meet, because of the slope and y-int of the first line (original line, I changed the numbers) the intersecting points was not a “good point”. So then I learnt from my failure and plotted a “good point” along my y=1 line and finished my equation from there.