As long as you do your work neatly and orderly, you shouldn't have much trouble with graphing linear equations. Here are some more examples.
First I'll do my T-chart. Since I am multiplying the variable x by a fraction that has 3 as its denominator, I will pick x-values that are multiples of 3. This way, when I plug in my value for x, the denominator will cancel out and I won't have fractions to deal with.
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Then I'll plot my points and draw my graph:
The variable x is multiplied by a larger value here; it's multiplied by 5. So I should expect that my y-values will grow fairly quickly. This means that I should expect a fairly "tall" graph.
First I'll do the T-chart.
This equation is an example of a situation in which you will probably want to be particular about the x-values you pick. Because the x is multiplied by a relatively large value, the y-values grow quickly. For instance, you probably wouldn't want to use x = 10 or x = –7 as inputs. You could pick larger x-values if you wished, but your graph would very quickly get awfully tall.
I can see, from my T-chart, that my y-values are getting pretty big on either end (that is, in the positive numbers above the horizontal axis, and in the negative numbers below). I don't want to waste time computing points that will only serve to make my graph ridiculously large, so I'll quit with what I've got so far. But I'm glad I plotted more than just two points, because lines that start edging close to vertical can easily go wrong, if I'm not neat in my work.
Here's my graph:
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I shouldn't let this equation or graph scare me. Yes, there is no "x" in the equation, but that's okay. I just think about it this way: it doesn't matter what x-value I pick; the y-value will always be 3.
My T-chart can look something like this:
No, I'm not going to plot the point (x, y) = (100, 3), but my T-chart emphasises the point for me. It doesn't matter what value I pick for x; the value for y is always going to be 3!.
This means that my graph looks like this:
Note: Any time you have an equation of the form "y equals a number", with no x in it, the graph will always be a horizontal line passing through the y-axis at a height of whatever that number is.
I shouldn't let this one scare me, either! Yes, there is no y in the equation, so I can't solve for "y =", but that's okay. The reasoning works just like the previous example. No matter what the y-value might happen to be, the corresponding x-value is always going to be 4. (Yes, I'm kind of working backwards, but that's okay. All I need are plot points. I don't always have to go forwards, from x-values to y-values, to get those points.)
So I'll do my T-chart backwards, picking various y-values, while always putting "4" as the corresponding x-values:
No, I'm not going to plot the point (x, y) = (4, 100), but the point emphasises for me that, for this line, all the x-values are going to be 4, regardless of what the corresponding y-value might have been. So my graph fills in like this:
Note: Any time you have an equation of the form "x equals a number", with no y in the equation, the graph will always be a vertical line passing through the x-axis at whatever that number is.
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