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## Lesson 100:  Introduction to Linear Equations

In this lesson we'll learn the very basics of what are called linear equations.  They come up again and again in math, so it's important to fully understand them.

A linear equation is an equation of the form y = mx + b.  m and b are specific numbers that will be provided, and x and y are variables.  If you are given a value of x, you can easily figure out the value of y.  You'll see that if you plot these (x,y) points on a coordinate plane and connect them, the result will be a line.

 x y (x,y) 1 5 (1, 5) 2 8 (2, 8) 0 2 (0, 2) -1 -1 (-1, -1) -2 -4 (-2, -4)

Let's look at the equation y = 3x + 2.  If we pick a value of x, we can easily figure out the value of y, by substituting the value of x in the equation.  For example, if x = 1, then y = 3(1) + 2 = 5.  If x = 2, then y = 3(2) + 2 = 8.  Let's make a chart with some values of x and y, and we'll also notate the results in (x,y) coordinate format.  This will help us to plot them on a graph.

It's usually a good idea to pick some positive values of x, and some negative ones, and also to see what y equals when x equals 0.

Sometimes a table like this is called a function table, or an in-out table.  What this means is that if you put a value of x into the equation, you get out a value of y.  X is our input, and Y is our output.  Note that in an equation like the one that we worked with, there is always one and only one value of y for any given value of x.

Later you'll learn how to plot the points that we found on a coordinate (x,y) plane.  If you do that, and connect the points, you'll see that they form a straight line.  This is why the equation is called a linear equation.  All equations of the form y = mx + b are linear equations, and they will always form a straight line.  The steepness of the line, and the place that it intersects the axes will vary depending on the values of m and b, but it will always be a straight (as opposed to curvy) line.

You'll work with linear equations much more later.  For now, just study the concept.

Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.

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