This year in math I would say I learned a lot academically but I also learned a lot about what works for me and what doesn’t when it comes to getting a good grade that I am proud of.  My top five pieces of advice that helped me a ton is to ALWAYS do the homework.  Throughout this semester I noticed that when I completed the homework I got a better result on my test.  Next tip is to pay attention in class.  A lot of the time if you don’t pay attention and then try to learn it on your own it seems to be a lot harder then it actually is.  Thirdly I would recommend revising every once in a while.  This ensures the marks on your midterm and final are going to be higher.  Fourthly make sure your final answers are always reasonable (this helped me a lot during word problems) and when having trouble I always like to think back to the basics.  Finally, if I were to give only one piece of advice to anyone it would be to ask questions and get help when needed.  I noticed when I did this it helped me tremendously and I did see a better result.  If you take all of these tips and apply them to your habits through anything you do I believe you will see improvement.

This week in math we learned about the elimination method.  Elimination is an important method when it comes to systems of linear equations, and is also quite simple.

When solving an elimination question you can either add or subtract the system. You always want to look for the easier solution and personally, I would add all the time. To solve an elimination question we need to have a zero pair.  So, a pair that cancels out.  In some cases the zero pair is given to us but in most cases you will have to multiple the other line (or sometimes both) with a common number.

After doing this you have a zero pair so all you need to do is add the rest. You then solve for X. So in this example, you will need to divide 88 by -40.  You then have the answer to your X variable.  But to finish the question off to find the solution you then need to go back to the original system and pick one of the equations, replace X with the answer you got and solve for Y.  After doing all this you then have the solution.

This week in math we learned three types of equations.  General form, Y-intercept form, and point-slope form.  They all tell us something different and some don’t tell us anything at all.

First, let’s start with general form. 0=ax+by+c. We like to call this form the pretty form because it is pretty useless. This form doesn’t tell us anything about our slope, Y-intercept or coordinates.  0=2x-5y+10, this is an example of a general form equation.  To tell this apart from the other equations general form always equals 0 and has to have a positive leading coefficient and can never contain fractions.

The second form is Y-intercept form.  Y=mx+b. This form is the most useful in my opinion when graphing.  This form gives you the slope (rise/run) and it also gives us the Y-intercept, which is our starting point on our graph.  Y= -2x/8 + 5, is an example of Y-intercept form.  The numbers paired with X is always going to be our slope, so in this case, the rise is -2 and our run is 8.  In some cases, you might come across an equation where -2 does not have a visible denominator, all this is saying is that the denominator/run is 1.  The equation is also telling us that our Y-intercept (starting point) is +5.  I know this is Y-intercept form because it has a Y on one side of the equal sign.

Lastly, point-slope form.  m(x-x)=y-y.  To use this form we need to know one point/pair of coordinates and the slope.  2(x-5)=y-3, is an example of the point-slope form.  In this example, 2 (2/1) represents the slope and (5, 3) are the coordinates.  I know this is point-slope form because it has brackets and uses only one pair of coordinates.  This form is the fastest to show an equation of a point on the graph.

This week in math we learned how to find the slope of two coordinates without using a graph. First, we should know that the slope is rise over run (rise/run). Another way you can look at it is height over width, Y over X.

To do this we used a thing called slope formula. Slope formula makes it extremely easy and possible when finding a slope with only two coordinates.

When using this formula you have to make sure to always have the Y coordinates as the numerator, and the X coordinates as the denominator as shown below.

You then subtract the coordinates from each other and you will end up with a fraction.  This fraction is representing your slope.  The rise is -6 and the run is 8.

(if it is a negative integer make sure to add it since a negative and a negative form a positive, as shown in the second diagram.)