This week in math, my class learned how to find the x-intercept and y-intercept of equations. It is a lot simpler than you would think, as all you need to do is when you want to find the x-intercept of an equation, you need to make the y (doesn’t matter where it is) zero. After that, you need to pull all the variables and the numbers on separate sides. As an example, if you want to find the y-intercept of y = 4x + 7, make 4 a zero, which will then give you an answer of -7/4. I got this because when I changed the x to a 0, I just needed to do -7 and 4, and since you can’t divide it, you would just put the fraction there. If you want to find the X intercept, it is the same thing, except you change Y to a zero. Another thing that I found out during this week was that to find out the slope of an equation, it will always be the number before the x and the intercept (y-intercept) will be the last number or the one without a coefficient.

1.  Graphing.

Before you even start graphing it, you need to make sure you have proper graph paper. The first step is to graph the first equation, typically on the left-hand side. The second step will be to graph the second equation, in the same area that you graphed your first one. The next is to figure out whether the lines are parallel, intersect or are on the same line. The last step to do is the check your solution. plug the second half into the first half of the question, and if there aren’t any issues, then you get the right answer. IF the lines insercept, make sure you not where that took place.

2. Substitution method

1. Solve one of the equations for either variable. Step two is to Substitute the expression from Step 1 into the other equation. The third step, the easiest, in my opinion, is the solve the resulting equation. Lastly,  substitute the solution in Step 3 into one of the original equations to find the other variable.

3. Elimination method

Firstly, you need to turn the 2 equations into standard form. This is similar to simplifying, except, you are making the number longer and easier to plug into other numbers. Then, you need to choose one coefficient to change to make it the opposite. After this, you need to eliminate everything else and that will give you your answer.

I found that doing the equations, personally, was a little bit challenging because they were hard to understand. To go more in-depth, the hardest part for me for finding the y intercept or in some cases even the x intercept. After a little bit of help from my parents, I learned to find the y-intercept you need to make x zero and usually divide the two remaining numbers. Something I found super easy was finding the slope from line to line in my equations. I feel that this was the easiest part of the whole project because we spent a lot of time working on it in class. I think that doing this project is good because it teaches us that not only is math a big part of our everyday life but is seen every day in our very own names. Lastly, to write my equations, i first wrote the y=, followed by the slope and intercept. In other words, i used y=mx+b to my advantage. I then had to use the slope for y and domain for x to shorten the line and make it fit perfectly into my shape or line.

This week in math class we learned about slope. The slope formula is rise/run and it is super important to remember that rise can be either to the top or bottom and run can be either left or right, depending on your teacher and the question.

If i am given the question to find the slope of 2/5, i would first find the lines that are both plotted in a corner (easy or good looking) and then use the rise over run formula to find the the slope. It is pretty simple atually. All you need to do is go up all thr way to the point you have chosen (or given) andthen go to the right or left, depending on the question. Thsi rise over run formula to find the slope is super easy to understand and is the foundations of this unit. If you don’t understand it, you are in trouble because you probably won’t be able to learn anything else because yes, almost every question, both easy and hard, will inlcude the rise over run formula. So get comfortable with it now!

This week in math was a bit of a struggle for me as some of the topics were difficult. But, as the week went along, and especially during the weekend, I felt that a light switch went off, and I started to understand some of the concepts in this unit. The biggest thing I got was understanding function notation and what it means/does. Function notation is, for example, f (4) = 0.  Before being able to write this, I had to put the 4 on the x-axis and the 0 on the y-axis. The next step for writing the f (4) = 0 is actually a lot simpler than you would, as you are just copying down what you just did. In other words, you are using your eyes to do the math. That is the other big thing I learned. 80% of this unit is just reading the question properly and letting your eyes do the math. In fact, like in this question, there is a lot of copying down and if you know what you are supposed to do, it is a lot easier than some people think. Another example where I let my eyes do the math was finding the domain and range to an ordered pair. To find the domain of 8,3, all you need to do is find 8 on the x-axis, then 3. Following this, you need to see what it is equal to. Lastly, it is very important to remember that the domain is x, and the range is y!

This week in math i learned how to put coordinates onto an x and y-axis graph. I will now show you how to solve a problem.

question = put 3 and 5 onto a graph

How to answer…

The first thing that you are going to want to do is to make sure you know which is a x-axis, and which is a y-axis. This is very important because if you don’t know, you will get the question wrong from the beginning. You also need to know that the middle of the graph is called the origin (see photo below) . Once you have determined this, (the x-axis is horizontal, the y-axis is vertical) you then need to place to coordinates into their respective spots. following this, you want to find where the 5 is ( x is always first) and put your finger where it is so you don’t forget. Then, as you probably are thinking, you want to find the 5 on the y-axis. from where your finger is, you want to put it up (because it is a positive) and go all the way up to the #5. Just like that, you have found your answer in quadrant 1!

For negatives, it is much simpler than you think, as all you need to do it work the other way and you will find your answer. It is not as difficult as exponents or multiplication! all you need to do it go the opposite direction, and it is pretty much the exact same question.

citation for image used = https://statisticsbyjim.com/graphs/x-and-y-axis/

This week in math, I learned how to master the distributive law and to determine the expansion of the expression. Originally I thought that I would do good on my test, but didn’t do as well as i hoped to. Doing the distributive law was one of my difficulties and after I got my test mark back, i realized this one was one of my weaknesses. I am going to show you how to use the distributive law. If my question is (x-4) (x² – 6x +3), I would start “distributing” the x into the x², 6x and 3. Following this, I would then put my 4 into the x², 6x and 3. Now, on my paper or whatever I am doing the question on, i should have two lines that look like x³, 6x² and 3x. My second line should look like -4x², 24x and -12. After simplifying these two brackets or terms, I need to simplify all of my numbers and variables to the simplest form. So, my final question now should be looking like x³ -10x² -27x -12. In other words, I am really just putting all the differences and multiplying them with their respective numbers and variables.

Here is a visual of the question.

This week in math I learned how to factor trinomial questions and here is one example of what I learned AND how to do it. My example is x² + 11x + 10. The first step is finding the factors of 10. To show this, for this question, the factors would be 10 and 1 and NOT 5 and 2 because 5 times 2 does equal 10 but only adds up to 7 which is not what the middle coefficient is. The other side 10 and 1 adds up to 11 and 10×1 equals 11 so therefore we would use it. In other words, those numbers must be able to be multiplied by each other AND added up by those numbers to make up the second number, in this case being 11. Following this step, it is pretty simple, as all you need to do is (x+10) (x+1). Is it very important to use the brackets. I also want to mention that if the variables were b, it would be (b+10) (b+1).

Below is a written example of how to do it.

This week, in my opinion, I learned a lot of new things. One of these things was learning how to simplify and evaluate a question with a number, and then two binomials in their own specific brackets. For example, 2(4x-3) (3x-4). For this equation, I would do 2 x 4x which would give me an 8x. Next, I would do the 2 x -3 which would give me an answer of -6. Next, I would re-write my formula, to make sure I am fully showing my work. This would be (8x -6) (3x-4). Following this step, I would use the “FOIL” to help me further simplify and to find the correct answer. FOIL represents “first, outside, inside, last). By doing this, the rest of the question is rather easy, if you use FOIL, that is. I would start by doing 8x times 3x, which would give me 24x². Next, I would do the “outside” which is 8x times -4. I get an answer of -32x. Following this, I would do the inside, which would be -6 times 3x, and the answer would be -18x. Lastly, I would do the “last questions of the terms. It would be -6 times -4, where the answer is 24. When I am done doing all of the steps above, I would put all the like terms together to further simplify. That would be, 24x²-50x+24.