## DesmosSignatureMath10FPC2021

This is a project I did in my Math 10 class, to practice graphing and linear relations. I used Desmos.com to create different equations that made lines on a graph. Each line made part of a letter, to spell my name.

**Write-Up:**

Creating my name out of linear equations was an interesting way for me to practice my math skills and be creative at the same time. I really enjoyed this project because I could be artistic, which usually isn’t connected to math. To create the equations for the slanted lines, I used point-slope form, which is *y-y**1**=m(x-x**1**)*. I also used the equations *x= *and *y= *to make horizontal and vertical lines. To change the height and length of the letters I wrote the domain or range of each equation. This allowed me to choose a specific point where each line could start and end. I decided to use all capital letters for my last name because they are a bit more simple to create. But for my first name I did the letters lowercase, so that they would look more unique. These letters were more difficult to create out of equations because there were a lot more lines for each one.

The main challenge I had was making the slanted lines for the letters like A, B, and N. I figured out that using point-slope form would be a good way to do this, because all I needed was the slope and one point. I chose the starting or ending point of the line and found the coordinates, then made them into an equation with the slope. Although I got stuck a few times, I kept trying out new combinations of numbers until I found something that worked. After a while this got easier for me and I was able to do it without help. The other challenge I had was lining up my last name under my first name, so they would take up the same amount of space and look centered. My first name has 9 letters and my last name has only 8, so I had to make the last name slightly larger. I calculated the distance my first name took up, and then divided it by 8 so I would know how big each letter should be. I started to create the equations for my last name, but I realized that it wasn’t working out and the letters weren’t lined up like I planned. I thought I had calculated everything correctly, but since it wasn’t working I decided to ask my Dad for help. He figured out that I hadn’t added on the space between each letter, so they were bigger than they were supposed to be. This was like an “aha” moment for me. Once I figured this out I just changed the domain and range of the letters to move them over.

After I had made all the letters, I decided to make it more artistic by changing the thickness and transparency of the lines. This made each letter look like slightly a different colour with an ombre affect. I learned a lot about relations and graphs from the assignment because I was creating each equation from scratch, rather than solving them in my textbook. Since my name is pretty long, I got a lot of practice writing equations that were different for every letter. I realized that every single line on a graph has a different equation. Overall, this assignment was a really enjoyable way to practice writing equations and see how they look on a graph.