Create a graph of the linear relation \(y=-2x+7\) using a table of values.
One option for graphing a linear relation is to create a table of values.
Now that we have our graph paper set up, we can plot the points from the table of values we created.
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Sometimes when we create a table of values, using the typical \(x\)-values of \(-2\), \(-1\), \(0\), \(1\), and \(2\) will result in corresponding \(y\)-values that are fractions. When graphing by hand we will want to avoid plotting points with fraction values because it is very difficult to do this accurately. It is not always possible to avoid fractions, however, in the following examples we will look at a couple of ways that we can try to ensure we have \(x\)- and \(y\)-coordinates that are integers.
Create a graph of the linear relation \(y=\dfrac{5}{3}x-1\) using a table of values.
In this example, to avoid plotting fractional values for \(y\), it's important to choose values of \(x\) that are multiples of \(3\).
If the slope of the linear relation is a fraction and the \(y\)-intercept is an integer value, choose values for \(x\) in your table of values that are multiples of the denominator of the slope. This will ensure the calculated values of the \(y\)-coordinates will be integers.
Create a graph of the linear relation \(2x-5y=15\) using a table of values.
\(2(-10)-5y\)
\(=15\)
\(-20-5y\)
\(-5y\)
\(=15+20\)
\(=35\)
\(y\)
\(=-7\)
Created with GeoGebra. Author: University of Waterloo. CC BY-NC-SA 4.0. https://ggbm.at/fkv5ywqz#
Let's take a moment to notice that in the previous worked examples, we used a table of values with five points. We really don't need that many points to graph a straight line. In fact, as long as we have two points for a linear relation, we can draw the line to represent the relation.
If we know at least two points on a line, we can graph the linear relation.
As we move through this lesson, you may start to notice that although creating a table of values will always work for you to graph a line, it will likely not be the fastest or most efficient method for you to choose.