Drawing straight line graphs

In a nutshell

Straight lines can be plotted by joining up points marked on a coordinate grid. Only two points are needed to plot a straight line, but more than two points can be used when sketching a straight line graph to add precision.

What is a straight line graph?

A graph is a series of points joined up, even if the points are not clearly marked (for example, with a cross). A straight line graph is the same, with the condition that these points sit in-line with each other. Another word for a straight line graph is a "linear" graph.

Plotting points

Points can be plotted from the origin on a coordinate grid. You move horizontally for the $x$ coordinate value, then vertically for the $y$ coordinate value.

Example 1

Plot the point $(-2,7)$ .

Starting from the origin, which is at $(0,0)$ , move horizontally by $-2$ , which means going to the left by $2$ .

Then, move vertically by $7$ , which means going up by $7$ . Mark this point:

Maths; Straight line graphs; KS3 Year 7; Drawing straight line graphs

Using only two points

If you plot two points, you can join them up with a straight line. The line should continue infinitely beyond these two points (in theory - obviously you can't actually draw an infinitely long line!).

Example 2

Draw a straight line that connects the points $(1,3)$ and $(4,0)$ .

Start by plotting these two points:

Maths; Straight line graphs; KS3 Year 7; Drawing straight line graphs

Then join these points up, ensuring the line continues past the two points:

Maths; Straight line graphs; KS3 Year 7; Drawing straight line graphs

Using more than two points

Sometimes you will be asked to plot many points and to join them up with a line. For now, this is how you will plot a straight line graph.

Example 3

Consider the table below, which gives a series of coordinates for points.

$x$	$-1$	$0$	$1$	$2$	$3$
$y$	$-6$	$-4$	$-2$	$0$	$2$

Plot these points and check that they all sit in a straight line.

The points you have are $(-1,-6)$ , $(0,-4)$ , $(1,-2)$ , $(2,0)$ and $(3,2)$ . Plotting these and connecting them looks like:

Maths; Straight line graphs; KS3 Year 7; Drawing straight line graphs

See that all of these points are indeed in-line with each other.