Plot points that satisfy a linear relationship

A point on the $xy$xy-plane represents a pair of quantities: the $x$x-value and the $y$y-value. We can write this pair in the form $\left(x,y\right)$(x,y) which we call an ordered pair. Given a set of ordered pairs, or a table of values, we can plot points on the $xy$xy-plane.

Exploration

Each column in a table of values may be grouped together in the form $\left(x,y\right)$(x,y), which we know as an ordered pair. Let's consider the following table of values:

$x$x	$1$1	$2$2	$3$3	$4$4
$y$y	$-2$−2	$1$1	$4$4	$7$7

The table of values has the following ordered pairs:

$\left(1,-2\right),\left(2,1\right),\left(3,4\right),\left(4,7\right)$(1,−2),(2,1),(3,4),(4,7)

We can plot each ordered pair as a point on the $xy$xy-plane.

Points plotted from the table of values

We can plot the ordered pair $\left(a,b\right)$(a,b) by first identifying where $x=a$x=a along the $x$x-axis and $y=b$y=b along the $y$y-axis.

Take $\left(3,4\right)$(3,4) as an example. We first identify $x=3$x=3 along the $x$x-axis and draw a vertical line through this point. Then we identify $y=4$y=4 along the $y$y-axis and draw a horizontal line through that point. Finally we plot a point where two lines meet, and this represents the ordered pair $\left(3,4\right)$(3,4).

Notice that in this example, each consecutive $x$x-value differs by $1$1 unit. In general, this may not be the case but the method for plotting these points remain the same.

Worked example

Consider the equation $y=-2x-1$y=−2x−1. A table of values is given below.

$x$x	$-2$−2	$0$0	$1$1	$4$4
$y$y	$3$3	$-1$−1	$-3$−3	$-9$−9

Plot the points in the table of values.

Think: Each column in the table of values represents an ordered pair. The ordered pairs are:

$\left(-2,3\right),\left(0,-1\right),\left(1,-3\right),\left(4,-9\right)$(−2,3),(0,−1),(1,−3),(4,−9)

Do: We plot each point by first identifying the $x$x-value along the $x$x-axis and the $y$y-value along the $y$y-axis. Then we can draw a vertical line through the $x$x-value and a horizontal line though the $y$y-value and plot where they meet.

Practice questions

Question 1

question 2

question 3