  # Graphing by Using a T-Chart

In graphing linear equations by using a t-chart, all we have to do is plug in random values for x and random values for y and get our points that way. So using a t-chart, we are going to draw a chart that looks exactly like it says, a "t". We place x on the left hand side and y on the right hand side so it easily becomes a nice point. Now, say for example I wanted to figure out what my x value would be if I plugged in a negative 1. So, for this, all I have to do for this is plug in a negative 1 for my y value and solve for x. I have x plus 2 times negative 1 equals 8. I have x minus 2 equals 8. So, x equals 10. Notice, now I have a point that I have to plot that as (10, minus 1). I go over 10 and then down 1. Here, I am on the far right hand side of the graph. So, let's see what would happen if I wanted to plug in something like a 4 for x. Now all I have to do is plug in a 4 for x and then solve for y. I have 4 plus 2 times y equals 8. This means that 2y equals 4. Therefore, y equals 2. Notice, all I am doing is plugging in any old numbers; it doesn't matter which ones you do. You'll always get an answer that has a point for it. Let's say that for y, I wanted a 3 there. So I have x plus 2 times 3 equals 8. So x plus 6 equals 8. This means that x is going to equal 2. So I have to plot the point (2, 3). I go over 2 and up 3. And I haven't plotted the point (4, 2) yet. So I am going to go over 4 and then up 2. So now, I have three points. You could have graphed this with two points, but I chose three, just to give you a "heads up" on all the different ways you can do this. All you have to do is draw a line through all of those points. Remember to draw the line far across the graph. So, this is graphing a linear equation by using a t-chart.

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