About jezmath

jezmath has been a member since December 10th 2010, and has created 155 posts from scratch.

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What Is Algebra?

Hello! Ever wondered what algebra is?

You may have an impression that algebra is math with nothing more than a bunch of symbols and letters.  I can understand if you think algebra is for the “birds” but trust me if it were not for algebra there would be no internet, iPhone and the other great material stuff in our world not likely exist.  So try to respect the subject as a powerful force for good!  I put together a video on what algebra is and how you can kind of think of the subject.  My goal is to show you that anyone can learn the topic with the right attitude and teacher.

 

Graphing Lines Using y = mx + b Slope Intercept

The most common way students learn to graph lines is using y=mx + b or the slope intercept method.  This is a great method because it’s straight forward and easy.  However a linear equation must be in y=mx + b form to use the slope intercept method of graphing.  Let’s look at a quick example.  The line 3x -7 = 2y is not in y = mx + b format so we could not use the slope intercept method to graph this line unless we rewrite it into y=mx + b which we can do without too much trouble.  Now let’s take a look at the line y=4x + 1 this line is in slope intercept y=mx + b form so we can easily graph it- how fun!  So how exactly do we graph a line in slope intercept form?  Well all we need to do is follow a few steps.  Ok step 1 is to plot the y-intercept( this is the point the line crosses the y-axis) and this number is the “b” pat of y=mx + b.  In our example y=4x + 1 the y-intercept would be 1.  Now onto our next step and for this we will use the “m” part of y=mx + b.  The “m” part is the slope of the line.  What we do is use the slope(rise/run) to plot a second point.  Specifically we count the rise and run from y-intercept to plot a second point (watch the lesson video to see how this is done).  Lastly we connect the two points we plotted and presto we have a line!  Graphing lines using the slope intercept method is a skill you must master so I really encourage you to relax and watch the lesson video below- good luck!


Concepts to remember about graphing lines using the slope intercept method:

1. the slope intercept method can be used when linear equations are written in y=mx + b form
2. the first step is to plot the “b” or y-intercept
3. next use the “m” or slope to find a second point
4. draw a line through the two points
5. if a line is not in y=mx + b form you simply can rewrite it such that it is and graph using the slope intercept

Graphing One Variable Linear Equations

Often it’s the easy things we tend to “mess up” and from my experience when students graph one variable lines they make mistakes not because it’s hard rather they just never remember if y = a number or x = a number is a vertical line or horizontal line.  Let’s do a quick review of graphing one variable lines.  If you are asked to graph a line that has the equation x=5 this would be a vertical line that goes through 5 on the x-axis.  Hence x= a number lines are vertical lines that goes through the respective number in the equation on the x-axis.  Now lets take a look at a like that is y = a number for example y = -2.  One variable linear equations where y= a number are horizontal lines going through the number. So in this example y= -2 would be a horizontal line passing through -2 on the y-axis. As I said from the start this stuff is easy but it’s also easy to confuse- take a look at the lesson below it should really help you memorize this once and for all!

 

concepts to remember about graphing one variable linear equations:

1. x= a number are vertical lines
2. y = a number are horizontial lines
3. vertical lines have no slope it’s what we call undefined
4. horizontial lines have a slope = 0
5. line equations are call “linear equations”

Basic Number Operations

Listen I would not like math if we did not do anything with numbers. Well fortunately we do things with numbers like add, subtract, multiply and divide. These “things” we do with numbers are called “operations”.  Now basic operators like addition and subtraction are not the only operators in math- actually there are many, many operations in advance math and even ones we can create on our own- how cool!  Anyways back to the basics. The thing you want to focus on while learning algebra with respect to number operations is key word phrases that go along with the operator.  For example the “sum” of 3 and 7 means to use the mathematical operation of addition to add 3 and 7 = the sum would be 10 of course.  However there are a few tricky areas with operators especially in division.  Make sure to watch the video lesson below for more help and good luck!


concepts to remember about number operations:

1. operations in math are simply the things we can do with numbers like add, subtract, multiply and divide.
2. the “sum” is the result of the addition operation
3. the “difference” is the result of the subtraction operation
4. the “product” is the result of the multiplication operation
5. the “quotient” is the result of the division operation

Translating Verbal Phrases Into Variable Expressions

Translating one language into another can be real fun especially if you’re on vacation.  So imagine if you will that your algebra class is located in some amazing location that uses a different language.  Well to communicate your teacher would have to translate one language into another language- word by word and phrases by phrases.  This task of translating is critical in mathematics and algebra as we take verbal sentences and write them as mathematical statements.  Here is a quick example:  “the amount of dogs (let D represent the number of dogs) in the house was increased by 10” could be written as “D + 10” . The key to translating any language is to know how to express one word into it’s equivalent in another language.  In this example we knew that the meaning of  “increased” was to add onto another value by using the “+” symbol.   If your confused don’t get stressed as many students first have a hard time with this topic- the lesson below will really help you so make sure you watch it……good luck!


concepts to remember about translating verbal and variable phrases:

1. memorize all the key phrases like “increased by” and “more than” and how to write these as mathematical statements
2. translating phrases are essential to solving word problems in algebra
3. sometimes a phrases will require two or more variables- don’t be shy to use more than one variable in your translation
4. translating verbal and variable phrases takes time and experience- don’t give up even if you struggle at first