Algebra 1 Graphing Linear Equations
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Now It All Lines Up
Graphing Linear Equations

 
 OK, up to now this X Y graphing hasn't been too exciting
 or too valuable, but here's the payoff.
 
 When we have an equation with just X's and Y's,
 that is, no exponents in the equation (like X 3 or anything)
 all of the X = this and Y = that solutions to the equation
 will be on a straight line on the graph!
 
 Once we have 2 points, we just draw the line that goes between them
 to get all of the possible X = this and Y = that
 solutions to the problem.
 
 The line (and the answers) go on in both directions forever.
 To show this, we always draw arrow heads 
 at the ends of the lines.
 
 So we can take the graph from the last page ...
 

 
 and do this!
 

 
 Let's do another one ...
 
 Example:
 

 -X + 4 = Y

 
 For the first X point, chose X = 0.

 It's usually the easiest one to do.

 

 -X + 4 = Y

-(0) + 4 = Y
4 = Y
 
 So we have X = 0, Y = 4.
 Mark it on the graph ...
 
 
 
 Did you notice that whenever X = 0
 the point is on the Y number line (Y axis)?
 Also if Y = 0 for a point
 it will be on the X axis.
 
 So we need one more point.
 Let's try X = 2 ...

 -X + 4 = Y

-(2) + 4 = Y
2 = Y
 
 So we have X = 2, Y = 2.
 Draw in that point ...
 

 
 Now with 2 points, we can draw in the line
 that all the X = this and Y = that points are on ...
 

 
 In the first example, the line was going up
 as it went from left to right.
 In this one, the line is going down
 as it goes from left to right.
 
 It sort of looks like the side of a hill
 OR A SKI SLOPE.
 
 Math people decided to call this "going up" 
 and "going down" thing the SLOPE of the line.
 
 WOW! A name that makes sense! Amazing.
 The names that other parts of the graph get 
 are harder to remember.
 
 The number lines themselves are called AXIS.
 The X number line is the X AXIS.
 The Y number line is the Y AXIS.
 The X and Y value pair numbers are called COORDINATES.
 The point where the X and Y number lines cross
 is called the ORIGIN.
 

 

   copyright 2005 Bruce Kirkpatrick

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