[HỌC TOÁN TIẾNG ANH] LINEAR EQUATION THE FUNDAMENTAL KNOWLEDGE

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Linear Equation: The fundamental knowledge

 

Linear equation is one the most basic topics of mathematics. For linear equation, you will learn about the relationship between two variables in one equation, in which the value of one of the variables depends on the value of the other; visual presentation of the relationship using graph, as well as its practical application. Relationships among different linear equations will also be covered.

 

In this video, I want to share with you the fundamental knowledge about 1 linear equation and the relationship between 2 different linear equations.

 

First, let’s learn some terminologies.

 

In linear equation, we usually use 2 variables or unknown numbers: x and y. Based on the situations in which these variables are used, they can take different meanings: score and learning time, population and total money in the country, the rate of increasing population…etc but whatever they are, we only have 1 basic formula of linear equation is y = mx + c.

Such equation forms a straight line in the plane.

 

In Vietnam, this formula is usually written as y = ax + b. m and a hold exactly the same meaning, just different ways of writing.

 

The meaning of m:

 

In the formula: y = mx + c, we call m gradient, or slope . This symbol tells us about how steep the line represented by the formula is . When m is positive, the larger m is, the steeper the line is. If m is negative, the smaller m is, the steeper the line is.

 

In calculation, m is calculated as changing in y divided by changing in x. In this line, we point 2 point A and B. We project A on Ox axis and B on Oy axis. This forms a right triangle. The value of m is changing in y divided by changing in x. Or if you have learnt about trigonometry, this is the tan of this angles.

 

From this calculation, we can easily recognise whether m is positive or negative based on the direction of the line. If the direction of the line is from bottom left to top right, the gradient of this line is positive. If the direction of the line is top left to bottom right, the gradient of this line is negative.

 

However, when the gradient is positive, we have two cases. Here and here. For positive m, the larger m is the steeper the line is; the smaller m is the less steep the line is. As a result.

 

It’s the other way around for negative m. The smaller m is the steeper the line is, and the larger m is the less steep the line is.

 

In the special case when the line is parallel with Ox axis, m = 0, and the equation becomes y = c

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