Onmatu- Pre-Calculus Article

Linear equations


Here is one simple example of a linear equation in two dimensional real space, R^2.
                           y = x.
How do we recognize a linear equation? It contains two variables, usually denoted by x and y. Sometimes you can find in literature a and b, but do not let that confuses you.
The point is that we have two variables and that they are of exponent one. That is, an equation
                       y = x^2
does not represent a linear equation. Similar with equation
                       y^2 = x + 4,
it is not linear equation.
A linear equation represents a line in coordinate system. So our first example of a linear equation, 
                             y = x
is a line that passes through points (0,0) and (1,1). How do we know this?
It is very easy! We need to find two points since this is enough for drawing a line. And how do we get them?
We choose one value for x, like we choose 0, and calculate the value of y based on a given equation. In our case y and x are the same, so y = 0. In the same way we get the point (1, 1).
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