Inverse Variations

The inverse variation is a relationship between two variables in which the final product is constant (a term or expression with no variables). As I said before as one value of one variable increases the other one decreases at the same time and in same proportion. The relationship is expressed as y=k/x. For example imagine that k=60. Y=60/X, so the table that expresses it would be:
X Y
3 20
6 10
12 5

And it would go on producing in a coordinate graph a line that is not straight but is curved. When the value of x is doubles the value of y is divided in half, making them to be opposite. One increasing and the other decreasing with a particular pattern. Another way to express the relationship of the inverse variations is to write it as: xy= k.

In problems that are such as: In a kick boxing test is evident that force=f needed to break a board varies with the lenght of the board= l. If it takes 5 lbs. of pressure to break a board of 2 ft. long, how many pounds would it take to break a 6 ft. long board?

Solving Linear and Inverse Variations

In mathematics the Inverse Variations have a different role that the Linear Equations but at the same time is as important as the Linear Equation role. In the other introduction I speak about the Linear Equations telling how to solve it in this topic is a little bit different. What does the word "Inverse" tell you? Means the opposite, solve the same thing but in the opposite procedure. Without using Inverse operations we wouldn't be able to solve relative equations for different coefficients and values.



I'm supposing you already know how to solve equations. When you think with mathematical models something really essential is to describe the relationship between variables by using tables and graphs to represent data. When solving Linear Equations you must have as an objective to develop a relative skill in solving equations with approximation and exact reasoning methods. What do I mean about this? Well when you have a graph with x and y variables and you want to find an exact value of a coordinate you must first look at the graph, the line would be a method to locate x and y would be seeing the line but that would only be an approximation method.

The Linear Equations

In mathematics the role that Linear Equations play is very important. Everybody knows that without math our life would be a disaster or at least would be much disorganized. But what’s the basis for all procedures and elements needed to perform mathematically something appropriately and correctly? Everything goes around the equations and for elemental problems specifically the Linear Equations.

The Linear Equations are basically made up of this following formula: y=mx+b. What does “mx” means? M is the slope if the equation and X means the x coordinate, the rise over the run in the line. And what those “b” means, well it is the y-intercept point. In the coordinate grid you would have to identify this quotient because is really basic and is essential for constructing the equation, but how do we find it? Easy you just see the first coordinate that crosses the y axis (horizontal).

The following question is very important. How do we find and calculate all of this? Is easy just you need to follow a simple procedure. For the slopes: You take two coordinates and do: y2-y1 and x2-x1 and your slope are ready. For the y-intercept without any graph you will do: y=x (m slope) + b then solve. Y= x + b and then do like terms, so you move b to left. B = x-y and then you have y-intercept. Without Linear Equations our lives would be a disorder and catastrophic events would occur daily.

Linear and Inverse Variation

Hello folks... My name is Jose Fernandez (I'm the Principal of a Middle School at USA) and I would like you to talk about the Linear Equations. My goal is to make sure the teachers would be able to teach the students this unit, by the way is a new unit we never taught our students in this school. My audiences are my teachers and my students that are going to learn this new unit.

My situation is that the owner of the school asked me (the Head of Middle School) to introduce this new Math unit because the school's level of Math in the student curriculum have been really low for the respective grades. My students are going to create a brochure explaining the different concepts on the new unit. They are going to create symbolic and word problems from this new unit, and last but not least they are going to make a project that proves in concrete examples their knowledge about the unit and applied them in any computer program they want.

The basic standards the students will use would be Microsoft Word and Macromedia Free Hand to create the word and symbol problems. The Microsoft Publisher is going to be used in the brochure with all the concepts learned on the unit. The final product would be a student choice between programs, in which they will apply their knowledge on concrete examples including a presentation. That would be the final project, thanks for seeing it and enjoy this blog!