# Plotting a Line Using a Rule Table

In this lesson we look at plotting linear graphs using a values table.

We have to make our own values table from an Algebra Rule that is given to us.

The rule always tells us how to calculate any y value from any x value that we have chosen.

To keep the mathematics simple, it is best to choose very small “x” values, such as: -2, -1, 0, 1, and 2.

Algebra Substitution Method

As a first example, let’s take a look at the line for the rule: y = x + 2.

We could also work out other y values using Algebra substitution.

We would use the x values -2, -1, 1, and 2 like this:

y = -2 + 2 = 0

y = -1 + 2 = -1

y = 1 + 2 = 3

y = 2 + 2 = 4

We could then make these into a set of (x,y) pairs and graph the line:

For x = -2, we obtained y = 0, and so our first point is (-2,0)

For x = -1, we obtained y = -1, and so our second point is (-1,-1)

and so on.

However, there is an alternative way of doing this process, where we make a Values Table, and do all our working out in the table.

We are still doing the same thing, but using a Table to do the Algebra Substitution.

Values Table Method for y = x + 2

We set up the usual values table for plotting points, but put an extra working out row into it.

Because y = x + 2 is a “one step equation” we only need one working out row.

It is a “one step equation” because only one thing is being done to x, and that is adding the 2 by the “+ 2″ next to x.

The working out row is shown in light blue below.

We also have a green row at the bottom for final answers.

Here is how we use the blue row for working out.

The next step is to do the working out for each box in the table, and write the answer each time into the purple “Y Value” row.

The final step to complete the values table is to write our numbers from the X and Y rows as (x , y) values.

We are now ready to plot our (x , y) values onto the Cartesian Plane.

We then extend the line, add some arrows to the ends, and create the finished straight line.

We also write the original “y = x + 2″ rule next to this line.

y = x + 2 was a fairly simple example, and many of us could have worked out the y values in our head, and not needed the blue working out row.

However, let’s look at a more involved fractions example, where working-out rows are definitely required.

Values Table Fractions Example

Here is a more involved example of an equation with several steps in it that involves fractions and negatives.

Because we have a three step equation, we need a working out row for each step like this.

The first working-out row is for multiplying “x” by negative one.

We now work on the second blue row, which is for the dividing by 2 step.

We take each answer we just got in blue row one, and divide it by 2, putting the answer into blue row two.

We are now onto the third working out step which involves adding 3 to everything.

Now we take our final worked out values from the bottom blue row, and copy them into the purple Y values row.

The final step to complete the table is to combine the original “x” values with the “Y” values, to create a set of (x , y) points.

Now we can start making our graph by plotting these points onto the Cartesian Plane.

We then complete the graph and write the original rule for the equation onto the graph.

Summary of Plotting from a Rule

Here are the steps required to plot any straight line graph from an algebra rule.

Values Table for Practicing Questions

Here is a blank Values Table you can print out or project onto a whiteboard to practice making Values tables from algebra rules.

Simply cross off and leave blank any working-out rows which are not needed for a question.

The full table of three working out rows should only be needed when we have an involved three step equation like y = 2x/3 + 5 .

(Clicking the Image should take you to an 800×594 pixels Table that can be projected or printed).

X-Y Grid for Practicing Questions

Here is a blank Cartesian Plane you can print out or project onto a whiteboard to draw the graph from your Values Table.

(Clicking the Image should take you to an 800×600 pixels X-Y Grid that can be projected or printed).

That’s it for this lesson. There can be a lot of working out to do, but if we follow the steps we should end up with a straight line graph each time.

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