We know how to identify if a table of values represents  a linear equation , and now we will look at how to display the same information on a number plane.
A table of values, created using an equation, forms a set of points that can be plotted on a number plane. A line, drawn through the points, becomes the graph of the equation.
We'll begin by creating a table of values for the following equation:
y=3x-5
The first row of the table will contain values for the independent variable (in this case, x). The choice of x-values is often determined by the context, but in many cases they will be given. To find the corresponding y-value, we substitute each x-value into the equation y=3x-5.
x | 1 | 2 | 3 | 4 |
---|---|---|---|---|
y |
Substituting x = 1:
\begin{aligned} y & = 3 \times 1 - 5\\ & = -2 \end{aligned}
Substituting the remaining values of x, allows us to complete the table:
x | 1 | 2 | 3 | 4 |
---|---|---|---|---|
y | -2 | 1 | 4 | 7 |
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.
To sketch a straight line graph we actually only need to identify two points.
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.
Consider the equation y=2x.
Fill in the blanks to complete the table of values.
x | -1 | 0 | 1 | 2 |
---|---|---|---|---|
y |
Plot the points in the table of values.
Is the relationship linear?
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.