Linear Equations

Linear equations are equations that, when plotted on a line graph, produce a straight line. They have simple variables like x and y and constants to relate to, like 2 or 3 but do not have indices or roots, since that would produce a curved line.

Of course, the actual algebra doesn’t matter as long as it simplifies down to something like that.

For example, y = 2x + 0.5 is linear, since it produces this:

graphsarenice

While y = x² + 1 is not, as it produces this:

curve

Also, x and y are not always used. Instead, any letter can represent x and any letter followed by the ‘x’ letter in brackets can represent y, so:

m(n) = 2n + 0.5    is the same as    y = 2x +0.5

This is called a function.

There are two (pretty simple) special forms of linear equations – identity and constant.

The identity function is f(x) = x. This means x and y are identical, producing a 45° line.

Constant functions are pretty self-explanatory. f(x) = C  – C can be any number, the graph will produce a horizontal line across from that number.

 

That’s about it.9722772_orig.jpg

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