unit 1.6  graphing relations
what we need to know
 Input/output tables
 Input = term numbers = Xaxis. It always is the first column on the table
 Output = terms = Yaxis. It always is the second column on the table
 Difference between expressions and equations
 Ordered pairs (X,Y)
 Xaxis is the horizontal axis
 Yaxis is the vertical axis
 A pattern: it repeats constantly
 Input = term numbers = Xaxis. It always is the first column on the table
 Output = terms = Yaxis. It always is the second column on the table
 Difference between expressions and equations
 Ordered pairs (X,Y)
 Xaxis is the horizontal axis
 Yaxis is the vertical axis
 A pattern: it repeats constantly
class notes


more information
what are linear relations?
LINEAR RELATIONS are relations (algebraic expressions) that, when graphed, result in a straight line (on whatever direction). Take a look at the following graphs:
Al graphs above are straight lines, and therefore are linear. Let's take a look at some nonlinear graphs:
As you can see, these graphs are mot straight lines, and therefore are considered nonlinear.
but, how can we tell if a graph will be linear from a table?
Linear relations, as I mentioned, result in straight lines when plotted. What this means is that for every constant change on the xaxis, there is a constant change on the yaxis. In other words:
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1 (or a constant pattern),Y increases by a constant rate (even if the pattern is different from the one on the xaxis), then a table is linear. This means, of course, that the relation is linear, and when plotted, you'll get a straight line. Let's look at the following tables:
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1 (or a constant pattern),Y increases by a constant rate (even if the pattern is different from the one on the xaxis), then a table is linear. This means, of course, that the relation is linear, and when plotted, you'll get a straight line. Let's look at the following tables:
Let's look at the patterns on the tables above:
steps to graph a linear table
 Complete the table of Input/Output table.
 Look at the first column,, the Xaxis. Determine whether the change from one number to the next is the same all the way through. That is, whether the pattern is constant.
 Do the same thing with the values of the OUTPUT column, which are the yaxis value.
 If, and only if, both the INPUT and the OUTPUT have patterns that are constant, then the RELATION IS A LINEAR RELATION. Again, the both have to have constant patterns.
 Once you determine that the table and the relation is a linear relation, it may help to make a column with the ordered pairs that you are going to use to graph.
Look at the following:
 Look at the first column,, the Xaxis. Determine whether the change from one number to the next is the same all the way through. That is, whether the pattern is constant.
 Do the same thing with the values of the OUTPUT column, which are the yaxis value.
 If, and only if, both the INPUT and the OUTPUT have patterns that are constant, then the RELATION IS A LINEAR RELATION. Again, the both have to have constant patterns.
 Once you determine that the table and the relation is a linear relation, it may help to make a column with the ordered pairs that you are going to use to graph.
Look at the following:
And so:
To graph:
 Get all ordered pairs.
 Plot the ordered pairs.
Here is what the graph for the table above looks like:
 Get all ordered pairs.
 Plot the ordered pairs.
Here is what the graph for the table above looks like:
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