Systems of Inequalities 2

Today in class we reviewed about systems of inequalities. We basically did a few problems and did more complicated ones when we got it down. All we have to do is afford not to make mistakes. In problems like these, one simple mistake like forgetting the negative or calculating wrong will not only give you the wrong answer, but cost you a lot of wasted time doing the problem wrong and doing the problem all over again. So now this is the time to be a perfectionist and let nothing distract you from making it perfect. 

Systems of Inequalities

Today in math class we learned about systems if inequalities. Well, more like a review now since we were on Thanksgiving Break and all. Mr. S gave us 7 steps for substitution. 1) pick variable. 2) Solve for variable. 3) Substitute. 4) CLT. 5) Solve. 6) Sub. into original equation 7) Solve. Technically he put 4 steps but I wanted to be very specific and put three extra steps. Now, the moment you've been waiting for...an example!


EX: 2x + 4y = 10
      x + y = 7  isolate your x! --> x = 7 - y
      2(7 - y) + 4y = 10
      14 - 2y + 4y = 10
      14 + 2y = 10
      2y = -4
      y = -2


Then to find your "x" you would put in substitute the "y" into the original equation.


EX: x = (-2) - 7
      x = 9


Then your coordinates are (9,-2). Simple, easy, and quick to do! Just don't mess up on your negatives...the process must be PERFECT!!!

Scatter Plots & Trendlines

Today in math class we learned about scatter plots and trend lines. Trend lines are a line of best fit and scatter plots are just plots scattered on a plane. We also learned that if a graph has two lines that are going up from left to right and are parallel, then it has a correlation. If there is a graph that just has plots scattered then it has no correlation.

Inequalities

Today in math class we learned about inequalities. But first we reviewed on changing point slope form to standard form. For inequalities, we learned that < means less than (we already knew that, but I can't say that for some of my fellow classmates) and > means greater than. Also that < means less than or equal to and > means greater than or equal to. We also learned how to graph them. For example: 2x + 4 < 10. You would subtract four from the problem so it would end up like: 2x < 6. Then you would divide by two to both sides and it would end up like: x < 3. When we graph it, you would put an open circle on 3 and draw a solid line going left on a number line.

Standard Form

Today in math class we continued learning on standard form. I've learned that when a slope is positive the coefficient is negative and vise versa. For example: y = 2/3x + 2 ---> 2x - 3y = -6. I think I've finally got a hang of standard form! Wow, big moment for me. I just love those moments when I get the lightbulb. It's just an awesome feeling to get!

Substitute & Equations

Today in math class we continued learning about slopes and graphs. Today Mr. S gave us a worksheet. We had to graph the equation given to us on the worksheet and tell if it is steep, if "y" decreases or increases, give the y-intercept, and tell if the slope goes up fromm left to right. The worksheet was basically very easy to understand after Mr. S went over some of the columns like telling if the "y" increases or decreases. We finished the worksheet in class and if we didn't finish it in class then we would have to finish it for homework. We also learned that if we substituted the coordinates in the equation: y = 3x + 1; (2,7) then we would know if the coordinates were right or not. For example, if we substited 2 for "x" in the equation and 7 for "y" then the equation would be true because 7 = 3(2) + 1 is a true statement. If the coordinates you substituted in aren't true then you would know that the coordinates are wrong.

Parallel & Perpendicular

Today in math class we learned about parrallel and perpendicular lines. We also learned how to write an equation that is parrallel and perpendicular. To tell if a line in parallel with another line is to see if they have the same slope. If they do then they are parallel lines. To write a perpendicular line, you just switch the slope. For example: y = 2x + b --> y = -1/2x + b. This is known as the multiplicative inverse. It is really simple and easy to do. We didn't go through much things today because most people in my class still can't find a slope. Anyways, I just hope I'm ready for the test tomorrow. Usually when Mr. S teaches us it makes sense, but the test is some crazy mojo.

P.S, S.I, & STD?

Today in math class we reviewd point slope and slope intercept and learned about standard slope. We learned how to change standard slope to slope intercept and vise versa. Here's an example: x + 4y = 16. To change it to slope intercept, you first need to isolate the "y" variable. So in order to do that, you divide by 4 for 4y and 16. That will then give you x + y = 4. But it is understood that "x" is 1 and so the slope intercept is:
y = -1/4x - 4 and there you have it! So to change -3/5; (-2,-4) to standard form. First you need to put it in point slope to find the y-intercept.

Example:
1.  y + 4 = -3/5 (x - -2)
2.  y = -3/5x +2 -4
3.  y = -3/5x - 5 1/5
So my standard form is 3x - 5y = 26.

Point Slope & Slope Intercept 2

Today in class we did point slope and slope intercept again. We also did problems on a white board. Mr. S just mainly gave us something like this: 3/4; (0,2). Then we would have to turn it into point slope form and graph it. So if we were to change this into point slope form it would look like this: y - y1 = 3/4 (x - x1). The original form of point slope is y - y1 = m (x - x1). So all I did was subsitute "y1" with 2 and "x1" with 0 and m with the slope 3/4. After you do all the math then you would end up with y = 3/4x + 2 or in slope intercept form. Then on the white boards we would graph it. So starting from the point (0,2) I would go up 3 and across 4. Why? Because 3/4 is y/x and rise/run. Since y is the rise we would go up 3 and x is the run then we would go across 4. We would start from (0,2) becuase that is a given point and when we graph it we can find the y-intercept.

Point Slope & Slope Intercept

Today in math class we reviewed on point slope and slope intercept. Mr. S gave us a Do Now that required us to make a equation and we had to know what to do and what we were doing. It was pretty easy, but most of the students in my class didn't know what to do and didn't ask questions. We wasted a lot of time and I basically sat there bored out of my mind watching them attempt to slove our Do Now that wasn't even that hard and the only way to get it wrong was 1) You weren't paying attention in class, 2) You don't know what to do and 3) You messed up somewhere in the problem. I know I sound like a complete nerd right now, but really? If you don't even bother to participate or learn in class, get the slope out of here!

Point Slope 2

Today in math class we went over point slopes and linear graphs again. We learned that a linear graph will always be a straight line, a absolute value graph will always be in a "v" shape, and that a quadratic graph will always be in a "u" shape. Whenever we see y = x, then it is a linear graph. Whenever we see y = x² , it is a quadratic graph. When ever we see y = IxI, it is a absolute value graph. Then after all of that was settled, we went on to just goin over what we did yesterday. We then graphed and did pretty much what we did yesterday.

Point Slope

Today in class we learned about point slope. The formula for point slope is:  y – y¹= m (x - x¹). So If I gave you something like this:  3/2;(4,8), you would substitute the values into the equation. y - 8 = 3/2x - 12/2 ----> y = 3/2x -6 +8 ----> y = 3/2x +2. So point slope isn't as bad as it sounds. All you mainly have to do is memorize the formula and substitute the values in. Since 4 in (4,8) is x, in the equation you would substitute 4 in x¹. Same thing goes for  8. You would 8 in y¹. Also your fraction would be your slope and in the equation y = mx + b, you would substitute m as 3/2.

Slopes 4

Today in math class we continued on slopes. Mr. S was gone for three days because he was really sick so almost a week without notes. He gave us some problems and we had to find with point doesn't belong by graphing and finding the slopes. To give you an idea, here's an example:

It's really all we got to today because some students in my class were confused. Then there was a fire drill that wasted 10 minutes of our learning time. Not really the best day ever.

Slopes 3

So today in class we continued to work on slopes. Mr. S gave us two input output tables with some missing numbers in the "y" column and we had to find the rule. The first rule was y = 4x-3. The second rule was y = 3x-2. Then we had to find the slope and graph it. So all we had to do was follow a formula and voila! We had our slope and we graphed it. So here is a visual picture of what I just explained for all you visual learners:

Then after that he gave us a mini-poster project due tomorrow. Pretty easy if you ask me.

Slopes 2

Today in math class we continued on learning about slopes. Once we got into the classroom he gave us a Do Now, which is just a problem we had to solve once we get into the classroom. The problems were pretty basic and easy to do. The first one was y = 3x-3. It was a blank input output table. We filled the first column, "x", with numbers from 1-6. Then we took the equation on top of the chart and filled the second column, "y", with 0,3 ,6, 9, 12, and 15. Then the second problem was y = 2/5x+2. We filled the "x" column with 1-6 like the first one. For the "y" column we put 2 2/5, 2 4/5, 3 1/5, 3 3/5, 4, and 4 2/5. Again, I know this is the worst explaination ever so here's a picture!

Slopes

So today in algebra we started a new unit. First he gave us an input output table with some missing spots in the "y" column. We then had to solve for "y" and then plot the points on a graph. Then when you connect the dots it should make a slope. A slope is really just a straight line. Mr. S then gave us a Co-Planar. Its basically just the steps we go through.
1) Locate y-intercept. 2) Use slope. 3) Locate three points. 4) Connect the dots. Our problem was 3/5x -3. So you move three points down. Then you move five points to the right and left. Then from the spot after coordinates (0,-3) move three points down. Your new coordinate will be (0,-6). After that look for (0,-6) and (5,0) and make a mark where they intercept. When you conncet points (-5,0), (0,-3), and (5,-6) it will make a slop. Okay I know that sounds really confusing maybe but teaching is hard! I don't know how Mr. S can do it all day! So here you go:

So here's how it SHOULD look like. FYI: if a line points left (down), its a negative line. And then if iit points right (up), its a positive line.

Function Notation & Matrices

Today in class we were told to find "f(x)". Since "f(x)" is just another way to say "y", all we had to do was substitute "x" with three since it said: Find f(3). Then we had to simplify all the equations and then multiply after that and then find the determinant. As always, I'm bad at explaining things so here is the problem in all of it's glory:

So after countless and countless attempts to find out this answer, it turned out that Mr. S had to give me the answer. I really hope I'm ready for the test tomorrow. Well, ready for it or not, bring it on!

Review!

So today in class we mainly reviewed for our math quiz tomorrow. We also did more exercises on multiplying matrices with negatives. And guess what? I think I've got all the negatives down! Finally! So we also went over some distributive properties and some really hard questions that are gonna be on the quiz. Though he didn't give us the answers, it's pretty easy but you really shouldn't mess up like writing down the wrong problem in your equation. So tonight I'm gonna study really really really really hard. Wish me luck! 

Multiplying Matrices

So today in algebra class, we learned how to multiply matrices. It's acually pretty easy. I was kind of fuzzy on it at first, but then once I started to retrace the steps and connet all the dots, it was SO EASY. Down side to it was that it took a long, long, long time. So again, I'm gonna just show you:

Determinents

So today in class we kept on learning about matrices and determinents. Turns out its too hot to work outside on the garden. But I hope we start on it soon because it will get more students to participate and actually look forward to school...maybe. Anyways we worked on matrices and equations. Its basically just finding "x" and "y" and solving the problem. Again, it's hard to explain so I'll just show you:

It's hard to get at first,but once you really sit and stare and think about it, it starts to make sense.

More Matrices...

Well, we have another day of matrices. Actually today was more easy to learn. One new thing we learned today was that equal matrices are matrices with the same dimension and elements. Pretty easy right? But nooooooo. After going through that, we have to find the determinant. What we do is we add the matrices together then we take the matrix and then we mulitply diagonally and then subtract the two products and we get the deterimant. Wait, what?

Matrices

Today in class we learned about matrices. They're pretty easy to do and kind of simple really. All you is match and add/subtract/multiply/divide.Also, we're gonna start a garden at the school! You're probably like, Dude what does a garden have to do with math? It actually has a lot to do with math. With how big you should make it, how many plants would fit in it, etc. We're gonna start on Monday and it's Texas. It's gonna be one HOT day.

Substitute

Another day with relations and functions. But mainly today we worked on equations and substituting in the variables. It's kind of hard for me to explain so I'll just show you.


EX:                   
               f(x) = 4x² - 2(x) + 5                                           
                                        f(4)


So all we had to do was replace all the "x's" with a four and solve it. So if you do the math correctly, the answer is 61.Just when I think I got the hang of it...the negatives come. Its still confusing my mind. I hate it so much that if i ever see it, I just skip it. Who wants to be a negative anyway? Positive is the way to go! 

Function Notation & Vertical Line Test

We continued learning about relations and functions today. This time though, Mr. S taught us a new way to know if the relation is a function by something called the vertical line test. Basically, if you draw a line going vertically on the graph of the relation and it crosses two different points, then the relation is not a function. Then he taught us about function notation. Saying that "f(x)" is "y". So everytime I see this: "f(x)" I know its "y". And there's a quiz coming up on Friday. For some wierd reason, I have a really bad feeling about it...

Relations and Functions

Today in class we talked about relations and functions. We also learned that a function table is almost like an input output table and kind of is. The "x" or domain is the input and the "y" or range is the output. It took me a while to get it at first, but I'm sure I've got the hang of it now. Except the whole integers thing throws me off. Oh negatives, why are you so confusing? If only I could find the cheat sheet Mr. S gave us last year. WHERE ARE YOU CHEAT SHEET?!?!