Did you know that you could graph a line based on a formula (y=m(x)+b)? The "m" in the equation is the slope, the "x" is the integer, and the "b" is the y-intercept. Take y=5x-3 as an example.  If the y intercept is negative, instead of the addition sign, it will be a subtraction sign. So now that we know the equation, how do we graph a line? Well, that is pretty easy to figure out. 
       First, you have to find the y-intercept. In this case, the y-intercept is -3. I know this because it is in the formula. Once you know that, then you could start graphing the line. You would start at -3, then go up 5 units. If the 5 was negative, you would go down 5 units. When you get to the location, you move 1 unit to the right. That's how you graph a line based on the equation. It's not that difficult to understand once you know the formula. 

      This topic was pretty hard for me to understand, but after researching and practicing, it became more easy for me. Once you know the equation of a line on a graph, you can find the slope, plug in other numbers to see if it will affect anything, or you can try an other equation. The first think you need to know before doing anything else is knowing the formula: y=mx+b. That equation will help you determine a line on a graph. Once you know that, you can find the slope. In order to find the slope, first thing you need to find is the y- intercept. That is pretty easy to spot because it is when the line passes through the y-axis. Then when you find that, you just simply start from there and search for other points that passes through that line. I still have trouble with these problems because it can get confusing with all the numbers and stuff you have to do. 
          Can you possibly figure out if the slope on the equation of the line is correct? That isn't really difficult to do at all. The first thing you would have to do is look at the slope that is given to you in the equation. If that slope is on the line, then that should be correct. 

      Which deal do you think is better? Well, a 12 pack of Mountain Dew at a local store is $4. 49 while a 1 liter of Mountain Dew costs $1.50. In my opinion, I would buy the 12 pack, and I have facts to prove that it is the better deal. For one, if you buy the 12 pack, you get 12 cans of Mountain Dew. But if you buy one bottle, it won't last for long. The way I figured out which deal is better is by using unit rate to compare these two deals.
         To set up a unit rate, you have to start with putting the price for each item under 1. So for example, it would be $4.49/1 and $1.50/1. The reason for that is because unit rate means 1 and you are trying to find the price for one item. So then you just divide. For the 12 pack you get 22 cents for one, and for the liter, well it's just $1.50 because it's just one. So the better deal is the 12 pack. The 12 pack is a much better deal because it is cheaper, and you get more than one for the price of $4.49. That is just about 3 more dollars than for one liter! You can use this  type of math to compare things, or when you want to find the cost of one item or thing. 

        The 1st semester has already passed, and now we're going into our second. I learned a lot of math topics in the past semester. The topic I remember the most was using a formula to find the unknown side, or the long side, of a triangle. I remembered this topic this most because it was easy and I remembered the formula very well. 
          Well, to find the measurement of the unknown side of the triangle, you have to know the formula. I know there is a name for it, but I just can't remember it right now. I know the formula pretty well though. It's a^2 plus b^2 equals c^2. The numbers that are already shown for the right angle and the base are plugged in to replace a and b. C represents the unknown side. For example, if the triangle had the measurements of 5 cm for the right side, and 2 cm for the base, it would be 5^2 plus 2^2 equals c^2. Once you get the answer from those numbers, you find the square root of it and that is the measurement of the hypotenuse. 
          This lesson was simple for me once I got the hang of it. All you really need to know is the formula, and where to plug in the numbers. What was confusing for me was when the hypotenuse measurement was given, and the right angle or base measurement was unknown. It was kind of difficult for me at first, but I got the hang of it. You have to use inverse operation to find the unknown side. 

      One of the most difficult math topics that I have learned so far is multiplying and diving with inequalities. Now to you, it may sound pretty easy, but for me, it was really difficult. At first, the multiplying was easy for me. All I had to do was multiply, and then bring down the correct sign. The variable also always comes before the sign and number. Now, that was easy. But the dividing part was the difficult part. There were many rules to diving with inequalities. Like if you divide with a negative number, you have to switch the sign. So say you were multiplying -6 by x which is greater than 48. You would divide each side by -6, and you get 8. So it would be x is LESS THAN 8.  I didn't get it at first because I couldn't remember that rule so I kept getting the answer wrong.
      But then, I finally found a solution to my problem. All I had to do was remember it. So I did. Now, it's too easy for me. I think I'm good at remembering things which really help me succeed in school. This math topic is really a piece of cake for me now, and I don't have much problems with it now. I thought I would never be able to accomplish it but I did. 

     Are you wondering what the Pythagorean Theorem is? Well, in case you haven't heard of it, it is a formula used to find the hypotnues, also known as the longest side, of a triangle. Don't understand it that well, yet? The formula is a^2 + b^2= c^2. It is very simple to use once you learn and get the hang of it. Now I'm going to give you a simple problem for example. If Bob traveled on his bike 2 miles north to the store, went back to his starting point, and traveled west  for 2 more miles to his house, what is the distance from the store to his house?  The distance from his house to the store is hypotnues. If you draw it out, it would look like a right triangle. So then you use the formula. You replace a and b with 2, then you just solve to find c. It is pretty simple. 
     Another example would be: a ladder is stood next to a building at  5 feet. The distance of the whole area is 10 feet. How high is the ladder standing from the ground? The 5 feet would be the hypotnues, so you replace that with c. Then you replace b with 10, and you solve for a. Pretty simple!

      Why are square roots called square roots? Well to start off, square roots is the factor that equals that number when it is times itself. So take 25 as an example. 5 would be its square root because 5 times 5 equals 25. I think square roots are called square roots because I think of it as a square; squares all have equal sides. If all sides of the square are the same, it would be the square root. I'm not sure if this definition is correct, but I think this is what it would most likely be similar too. Another name that could replace square roots is perfect squares. Perfect squares are when the square root is not a decimal or fraction. For example, 4, 16, 25, 49, etc are perfect squares because their square roots are perfect; they aren't decimals or fractions. 

     Awhile ago  my math teacher taught a lesson about negative exponents. She said that you can not work with them. In order to get rid of the negative, you have to make it into a fraction. To do that, you must add 1 underneath the whole number. Then it becomes a fraction, and it usually is less than 1. Take 5^-2 as an example. You would put a 1 below it to make it a fraction. Then it becomes 1 over 5^2. The negative is no longer there. After that, you just simplify and you get 1 over 25. That is why 1 over 25 is less than 1 because it is just a part of whole.  You could also just multiply one-fifth times one-fifth and you will still get the same answer. I think that method is pretty easy to do. This math lesson really helped me understand the value of negative exponents and how to get rid of them and make them become fractions.

      What do I know about exponents? Well, I don't know that much about it, but I do know that it is used in math and it's one big number with a smaller number on top of it!  I also know that when you pronounce it, it has to be "to the power of." For example, two to the third power. That means that two is the whole number (big number) and three is the exponent (small number). I haven't really had a lot of practice with exponents, but I do know how it works. 
     The whole point of exponents and "to the power of" is simply meaning that that whole number, the big one, is being multiplyed by what ever the power is. Take one to the third power for an example. That means that one is being mulitipled three times. Now, you're probably thinking, why not just mulitply it by 3? Well, in this case, it would be the same answer, but in others, it won't. For example, there is an exponent that is seventh to the second power. It is not seven times two, it is seven times seven. You get two different answers from both of these problems. 
     I have previously done this in sixth grade, I think. So this is all I could really remember of it. Hopefully, I get to learn more about exponents and refresh my mind. 

     For today's math blog, we were to play this very interesting math game. In that math game, you were suppose to find the difference of the two numbers that was on that side the of the frame; there was a total of four numbers in each frame. There were also 3 levels: integers, fractions, and decimals. The one that was very easy for me to figure it out was the level with the integers. I think that was level was the easiest for me because I understand all the rules when adding, subtracting, mulitplying, and dividing integers. For example, the problem was -2 subtracted from 7. I knew the answer to that was 5 because 7 was the largest number and it was positive. The sign of the answer always comes from the largest number. I had no difficulties while playing that level. 
     I did have some problems with the other two levels, though. The most difficult one for me out of the three levels was the fractions. I think I had the most trouble with that one because some of the fractions did not have common denominators. I have yet to learn how to subtract fractions with unlike denominators in an easy and fast way. I eventually found out though because I looked online. The easiest way was to cross mulitply, and then add, and then add the denominators for the common denominator. I found that very easy and it also worked. I'm glad I learned how to do that because it is very helpful. 
    I didn't have much trouble with the decimals, expect that some numbers had me thinking for awhile. I think the reason why I had trouble was because there was more than one number and there was a decimal. But overall, I enjoyed playing that math game.