Lesson How to graph linear equations

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%5E1

.)
Here's the graph for y+=+x+-+9

graph%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x-9%29+

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+%2F+run

. I'll give you another nice graph.
graph%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B1%29+

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%2F1

, 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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B4%29+

graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B4%29+

The slope is ___
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-1%29+

The slope is ___
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B4%29+

The slope is ___
Slopes can also be negative:
graph%28+600%2C+600%2C+-7%2C+7%2C+-7%2C+7%2C+-3x%2B5%29+

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+=+%28b+-+d%29+%2F+%28a+-+c%29

So, for the coordinates (0, 5) and (3, -4),
m+=+%285+-+%28-4%29%29+%2F+%280+-+3%29

The slope is negative 3!
TRY IT YOURSELF:
Find the slope of:
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%29+

The slope is ___
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-1%29+

The slope is ___
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-4x%2B4%29+

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%2A0-1

-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%2A1-1

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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+1%29+

(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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

Graph 2x + 1 using way 1:
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

Graph 4x + 5 using way 1:
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

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%2F1

, 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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x+%2B+4%29+

(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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

Graph 2x + 6 using way 2:
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

Graph 3x - 4 using way 2:
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%29+

That was EASY! Next lesson: 2x2 systems of equations! BYE YOU ALL!

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