How to Graph Linear Equations

Linear equations are the most basic algebraic equations in Algebra I, and they are also the most basic equations to graph. As indicated by its name, graph of a linear equation is a straight line. It’s important to know that any two points define the position of a straight line. In other words, as long as we can find two points from the equation, we can locate the line in graph.

Example: To graph linear equation Y = 2X + 1.

1). Choose the two easiest points from this equation: (X1, Y1) and (X2, Y2).

      The points are: (0, Y1) and (X2, 0).

      The point (0, Y1) means that when X=0, then Y=Y1.  We choose this point because when X=0, we know that on the graph, this point is surely on y-axis. That is to say, on the y-axis, every point has X = 0.                                                                                  

 

        |y
        |
        |
___________  x
        | o
        |
        |

 

           (Every point on the red line in this graph has X=0.)

 

           The point (X2, 0) means that when Y=0, then X=X2.  We choose this point because when Y=0, we know that on the graph, this point is surely on x-axis. That is to say, on the x-axis, every point has y = 0.                                               

          (Referring to the graph above, every point on the black line has Y=0.)

 

  2). Solve for these two points. --- Simply plug either X=0 into the equation to solve for Y, or plug Y=0 into the equation to solve for X.

        Point (0, Y1) says X=0, so plug it into the equation of Y=2X+1     à    Y=2*0 +1 = 1.

So here we’ve solved that Y=1 when X=0. In other words, this point is (0, 1).

        Point (X2, 0) says Y=0, so plug it into the equation of Y=2X+1     à    0=2X +1  à   X=-0.5

So here we’ve solved that X=-0.5 when Y=0. In other words, this point is (-0.5 , 0).

 

3). Graph!

     Now that we’ve found two points for this equation, we can put these points on the graph and simply connect them with a straight line going all the way to both ends. At this point, you’ve done your job nicely!

 

 

 



  • Subject : Math
  • Topic : Algebra 1
  • Posted By :
  • Created on : 01-27-2011

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