This lesson is a refresher on how to graph a line.  There are several ways to graph a line.  They are:

1.  Finding 3 points and graphing them (using an x,y chart)

2.  Using the slope and Y-intercept

3.  Using the X and Y intercepts

Lets start with using an x,y chart to find 3 points.  Lets use the equation, 2X + 4Y = 8.  The easiest thing to do is get y by itself first.  So subtract 2X and then divide by 4 to get:  Y = -½x + 2. It is easier to graph whole numbers and smaller numbers rather than large numbers...so lets start by substituting 2 in for X .  This gives us:  Y = -½(2) + 2, which gives us Y = 1.  So that gives us the ordered pair ( 2, 1).  Next lets substitute 4 in for X since even numbers will allow us to get whole numbers for Y.   So if you substitute 4 in for X, you get Y = -½(4) + 2 which equals 0, so we have the ordered pair (4, 0).  And lastly, if we substitute -2 in for X, you get Y = -½(-2) + 2 which equals 3, so we have the ordered pair (-2, 3).   Graphing these three ordered pairs and connecting them gives us the following line:

So the first thing we do is graph the number 2 on the Y axis since it is the Y-intercept.  Then we use the slope of -½ to count over and either up or down to get another point on the graph.  As we recall, the slope represents rise/run or (the change in y)/(the change in x).   So from the 2, count over to the positive direction 1 and down 2 or over to the negative direction 1 and up 2.  (Only use the negative either with the top or the bottom...not both at the same time or you would have two negatives which would make a positive slope.)

Use this information on the cartesian coordinate system and your line should look like this:

The third way is to find the X- and Y-intercepts and graph them.   You can do this with the equation just as it is:  2X + 4Y = 8.  First substitute 0 in for X and solve for Y.  This will give you the X-intercept.   Then substitute 0 in for Y and solve for X. This will give you the Y-intercept.  Then you can plot these two points and connect them to graph the line.  Try it and check your answer below.

Substituting 0 in for X, we get:  2(0) + 4Y = 8....so 4Y = 8 giving us Y = 2.  This gives us the ordered pair (0, 2).

Substituting 0 in for Y, we get 2X + 4(0) = 8 giving us X = 4.  This gives us the ordered pair (4, 0).  Plot these two points and connect them to get the following line:

Since you get the same graph no matter which method you use, chose the method that is easiest depending on the form of the equation.  If Y is already by itself, either use the slope and Y-intercept or the x, y chart.  Sometimes it is easier to use the slope and Y-intercept if it is hard to get away from fractions.  If the equation is in standard form ( the x and y are on the same side of the equal sign) it is usually easier to get the X- and Y-intercepts.

So lets practice it a few more times.

Suppose we are given the equation Y = 3X - 4....Which method would you use?  Try it and check it with the answer below.

Since Y is already by itself, it is probably easiest to either use the slope and Y-intercept or make an x,y chart.  Using the slope and Y-intercept, we use the fact that the slope is 3 (the number in front of the x) and the Y-intercept is -4.  We start by plotting -4 on the Y- axis and then count up 3 and over to the right 1 since 3 = 3/1, making the change in y 3 and the change in x 1.  Since they are both positive, make sure you count both in the positive direction each time.   Your line should look like this:

If the equation of the line is 3X - 4Y = 12, which method would you use?  Try it and check it below.

Since this equation is in standard form, I would recommend using the X- and Y-intercepts.  So substituting 0 in for X, we get -4Y =12, so Y = -3 giving us the ordered pair (0, -3).

Substituting 0 in for Y, we get 3X = 12