Introduction
Remember that a table of values can be constructed by substituting multiple values into a  linear equation . Once a table of values has been constructed, the table can then be used to create a graph.
Plot points from a table of values
Each column in a table of values may be grouped together in the form (x, \, y). This pairing of numbers is known as an ordered pair.
Let's plot the ordered pairs from the following table of values:
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | -2 | 1 | 4 | 7 |
The ordered pair, (a, b), is plotted on the number plane by first identifying where x=a is along the along the x-axis, and where y=b lies along the y-axis.
By plotting points on the number plane that correspond to ordered pairs from the table of values, a straight line can then be drawn that passes through each of these points.
To draw a line from a table of values, it is useful to plot the significant points and draw the line that passes through them.
Consider the following linear equation:y = - 6 + 3x and the following table of values:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | -6 | -3 | 0 | 3 |
There are two significant ordered pairs, namely the x-intercept and the y-intercept.
The x-intercept has the form \left( a, 0 \right) which is a point that lies on the x-axis.
The y-intercept has the form \left( a, 0 \right) which is a point that lies on the y-axis.
The x-intercept in our example is \left( 2, 0 \right) and the y-intercept in \left( 0, -6 \right).
The line represented by equation y = - 6 + 3x can be graphed by drawing a line which passes through these two points.
Examples
Example 1
Consider the equation y=4x. A table of values is given below.
| x | -2 | -1 | 0 | 1 |
|---|---|---|---|---|
| y | -8 | -4 | 0 | 4 |
Plot the points in the table of values.
Is the graph of y=4x linear?
Each column in a table of values may be grouped together in the form (x, \, y). This pairing of numbers is known as an ordered pair.
We can complete a table of values by substituting each x-value into the given equation.
To plot a point, (a, b), on a number plane, we first identify where x=a lies along the x-axis, and where y=b lies along the y-axis.
When checking if a set of points forms a linear relationship, we can choose any two of the points and draw a straight line through them. If the points form a linear relationship then any two points will result in a straight line passing through all the points.
There are two significant ordered pairs, namely the x-intercept and the y-intercept.
The x-intercept has the form \left( a, 0 \right) which is a point that lies on the x-axis.
The y-intercept has the form \left( a, 0 \right) which is a point that lies on the y-axis.