There are several ways to graph a straight line given its equation.   

Let's quickly refresh our memories on equations of straight lines:

Slope Intercept Form Point Slope Form Horizontal Lines Vertical Lines


when stated in "y=" form, it quickly gives the slope, m, and where the
line crosses the y-axis, b, called the y-intercept.


when graphing, put this equation into "y = " form to easily read graphing information.

y = 3 (or any number)
horizontal lines have a slope of zero - they have "run", but no "rise" -- all of the y values are 3.

x = -2 (or any number)
vertical lines have no slope (it does not exist) - they have "rise", but no "run" --all of the x values are -2.

Graphing Tidbits:

If a point lies on a line, its coordinates make the equation true.

(2,1) in on the
line y = 2x - 3
because 1 = 2(2) - 3

 

Before graphing a line, be sure that your equation starts with "y=".

To graph 6x + 2y = 8
rewrite the equation:
2y = -6x +8
  y = -3x + 4
Now graph the line using either slope intercept method or chart method.

The x-coordinate may be called the abscissa.

The y-coordinate may be called the ordinate.

 

Methods of Graphing a Line

Using  y = mx + b
with rise/run
Using a Chart -
Plotting Points

Graph  2y = 6x + 4

1.  Put your equation in "y=" form.
                     y = 3x + 2

2.  The number in front of x is the slope.
     (If necessary, place this number over 1 to
      form a fraction for your rise/run.)
                    slope = 3/1       

3.  The "b" value is where the line crosses the
     y-axis.  Be sure to check the sign of this
     number.    b = 2
                   
4.  Plot the b value on the y-axis.
                    see graph below

5.
  Standing at this point, use your rise and run
     values to plot your second point.
     (If rise is positive, move up.  If rise is negative,
      move down.)
     (If run is positive, move right.  If run is
      negative, move left.)

6.
  Connect the two points to form the line.



 

Graph  2y = 6x + 4

X Y
-3  
-2  
-1  
0  
1  
2  
3  

Create a chart to hold x and y values from your line.  For lines, the x-values usually range from -3 to +3, but may be any values you wish.

While charts often contain more than 2 entries, only two entries are needed to determine a straight line.  A third point should be used to "check" that an error was not made while computing the first two points.

X Y
-3 -7
-2 -4
-1 -1
0 2
1 5
2 8
3 11

Substitute the x-values into the equation to determine the y-values.  Putting the equation in "y=" form first will make the substitution easier.
y = 3x + 2

Now start substituting.  For example, substitute x = -3:
y = 3 (-3) +2 =  -9 + 2  = -7

  Plot the (x,y) coordinates to graph the line.

 

See how to use your
TI-83+/84+ graphing calculator  for basic graphing.
Click calculator.