Straight line graphs
The graph of each of these equations is a straight line:








If an equation can be rearranged into the form
, then its graph will be a straight
line.
In the above:
can be rearranged as
(which can be re-written as
can be rearranged as
).
.
can be rearranged as
or
.
Vertical and horizontal lines
Vertical lines have equations of the form
Horizontal lines have equations of the form
.
.
Example
Draw the graph of
.
Mark some points on a grid which have an -coordinate of 3, such as (3, 0), (3, 1), (3, -2).
The points lie on the vertical line
Lines in the form
where
and
.
are vertical and lines in the form
are numbers.
are horizontal,
Plotting straight line graphs
A table of values can be used to plot straight line graphs.
Example
Draw the graph of
Create a table of values:
x
.
-1
0
y
1
2
3
2
5
8
Plotting the coordinates and drawing a line through them gives:
This is the graph of
.
Sketching straight line graphs
If you recognise that the equation is that of a straight line graph, then it is not actually
necessary to create a table of values.
Just two points are needed to draw a straight line graph, although it is a good idea to do a
check with another point once you have drawn the graph.
Example
Draw the graph of
.
If you recognise this as a straight line then just choose two ‘easy’ values of , work out the
corresponding values of and plot those points.
When
,
. Plot (0, −1).
When
,
. Plot (2, 5).
Drawing the line through (0. -1) and (2, 5) gives the line above.
Example
Draw the graph of
.
If you recognise this as a straight line then:
When
, then
means
, so
. Plot (0, 4).
When
, then
means
, so
. Plot (6, 0).
Draw the line through (0, 4) and (6, 0).
Now check:
The drawn graph passes through (3, 2).
Does (3, 2) satisfy
does equal 12, so we can be confident that our line is correct.