Lesson How to graph linear equations

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This Lesson (How to graph linear equations) was created by by jam123(18)

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About jam123: I teach you, but also these questions I make up teach me!

OK, I'll give you a lesson for graphing linear equations. (couldn't really think of a good intro)
Anyway, to check if a polynomial is a linear equation or not, check its degree (the highest exponent)
If its degree is 1, it's a linear equation.
Ex.
{{{y = x - 9}}} is a linear equation because it has a degree of 1. (x has an exponent of 1. You can read x as {{{x^1}}}.)
Here's the graph for {{{y = x - 9}}}, 
{{{graph( 600, 400, -10, 10, -10, 10, x-9) }}}
It was a line, right? That means it's a linear equation!
OK, how do we graph them?
The basic formula for graphing lines is:
{{{y = mx - b}}} where m is the slope of the line and b is the y-intercept.
...you'll understand later.
ANYWAY, graphing linear equations are really easy when you find out how to, so here goes!
We can think of the slope of a line as {{{rise / run}}}. I'll give you another nice graph.
{{{graph( 600, 400, -10, 10, -10, 10, x+1) }}}
When the line hits the coordinates (-1, 0), it goes up 1, and goes right 1. You can rise up or down, but you always run RIGHT! Which means the slope is {{{1/1}}}, which is 1! The slope is 1! We always have to find points on the line with no decimals then find the slope!
TRY IT YOURSELF:
Find the slope of:
{{{graph( 600, 600, -10, 10, -10, 10, 2x+4) }}}
The slope is ___
{{{graph( 600, 600, -10, 10, -10, 10, 3x-1) }}}
The slope is ___
{{{graph( 600, 600, -10, 10, -10, 10, x+4) }}}
The slope is ___
Slopes can also be negative:
{{{graph( 600, 600, -7, 7, -7, 7, -3x+5) }}}
The line hits the coordinates (0, 5) and (3, -4). The formula for finding slopes is:
For the coordinates (a, b) and (c, d)
{{{m = (b - d) / (a - c)}}}
So, for the coordinates (0, 5) and (3, -4), 
{{{m = (5 - (-4)) / (0 - 3)}}}
{{{m = (5 + 4)) / -3}}}
{{{m = 9 / -3}}}
{{{m = -3}}}
The slope is negative 3!
TRY IT YOURSELF:
Find the slope of:
{{{graph( 600, 600, -10, 10, -10, 10, -x+4) }}}
The slope is ___
{{{graph( 600, 600, -10, 10, -10, 10, -2x-1) }}}
The slope is ___
{{{graph( 600, 600, -10, 10, -10, 10, -4x+4) }}}
The slope is ___
Now we learn how to graph a linear equation.
There are 2 ways. I'll show you the easiest way first.
WAY 1
Just substitute x for 2 values then plot the points on the graph!
Ex. graph y = 2x - 1
Let's substitute x for 0 and 1.
OK, the x coordinate will be 0 and 1.
So far, our coordinates are (0, y) and (1, y)
But what's y?
Remember -- we substitute! Let's try 0 first:
{{{2*0-1}}}
{{{0-1}}}
-1!
If we substitute x for 0, we get y for -1!
So far, our coordinates are (0, -1) and (1, y)
Let's do 1 now:
{{{2*1-1}}}
{{{2-1}}}
1!
If we substitute x for 1, we get y for 1!
Our coordinates are (0, -1) and (1, 1)
Then, we plot the points on the graph and get this:
{{{graph( 600, 600, -10, 10, -10, 10, 2x - 1) }}} (See how the coordinates [0, -1] and [1, 1] touch the line? That means it worked!)
Is it that hard? NO!
TRY IT YOURSELF:
Graph x + 2 using way 1:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
Graph 2x + 1 using way 1:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
Graph 4x + 5 using way 1:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
WAY 2:
Remember the formula of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept
Well, the y-intercept is the point where the line collides with the y line.
Let's try graphing 2x + 4.
4 is the y-intercept, so we plot a point on the graph: (0, 4).
2x is the slope: 2 is really {{{2/1}}}, so we go up 2 from the y intercept, then go right 1. Our new point is (1, 6).
Now connect the lines and here's our graph:
{{{graph( 600, 600, -10, 10, -10, 10, 2x + 4) }}} (See how the coordinates [0, 4] and [1, 6] touch the line? That means it worked!)
TRY IT YOURSELF:
Graph x + 1 using way 2:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
Graph 2x + 6 using way 2:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
Graph 3x - 4 using way 2:
{{{graph( 600, 600, -10, 10, -10, 10) }}}
That was EASY! Next lesson: 2x2 systems of equations! BYE YOU ALL!