Characteristics of straight lines
Lesson overview
Outcomes
This activity encourages students to make links between the
equation of a line and the graph of the equation. Students graph
various lines and make comparisons between them looking at the
gradient (m) and the y-intercept (b). Discussions about similarities
and differences between graphs and equations should lead students
to draw conclusions about how the various components of an
equation affect the way it will appear on a graph.
Stage 4
Software used
PAS 4.5 Graphs and interprets linear
relationships on the number plane.
Stage 5
PAS 5.1.2 Graphs simple linear and nonlinear relationships from equations
PAS 5.2.3 Applies the gradient/intercept
form to interpret and graph straight lines.
SMART Notebook, GeoGebra, OneNote
Stage 6
AM2 Modelling linear relationships
Activity A
Step 1
Decide how you would like the students to graph
lines: GeoGebra, MS Math 3.0, graphics calculator
or pen and paper.
Step 2
Demonstrate to students how to graph the
equation of a line in the format chosen (paper,
GeoGebra, MS Math 3.0 or a graphics calculator).
Step 3
Students open the SMART Notebook file,
Characteristics of straight lines, and flip to the first
workspace.
To record this – clip into OneNote or save the page
in the SMART Notebook file.
Step 4
Ask students at random, drawn from a hat, to come
to the front and show the class their choice of
equations and explain the characteristic the
equations have in common.
Step 5
Ask students to work in pairs to come up with
atypical, unusual or different groupings of
equations which they show to the class. The class
then suggest what characteristic the equations
have in common.
Activity B
Step 1
Students flip to the second workspace.
Individually, students create their own set of
equations.
Students work in pairs to decide which groups of
equations have something in common. (one laptop
between two students)
Once they have made their decision they can drag
the equations into the right hand box and type the
characteristic into the box below it.
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Step 2
PART E
Students swap computers with another student
and try to group the equations, checking each
group formed with the original student for
confirmation.
Step 1
Students flip to the fifth workspace. Individually,
students create their own line graphs.
Step 3
Record groupings using OneNote clips or save the
page in the SMART Notebook file.
Activity C
Step 1
Students flip to the third workspace. Individually,
students come up with a characteristic, illustrate
using a picture (perhaps using line tools) or in
sentence form and then produce another set of
equations which all adhere to the characteristic
given.
Step 2
Students swap computers again and group graphs
with similar characteristics, giving reasons and
recording results.
Teaching notes
Parts A, B, C, D and E may be used in one lesson
or as activities in separate lessons. Choose the
most suitable activities for your students.
Activity D
There are two main responses students are likely
to give. They will either choose properties of the
equation that are similar e.g. both have an x
coefficient of 2 or they will choose equations that
produce similar graphs (both lines slope to the left).
Be willing to accept both forms of response but
guide students to explore a range of
characteristics.
Step 1
Questions to ask
Step 2
Record completed workspace.
Students flip to the fourth workspace. In pairs,
students drag graphs which have a similar
characteristic into the space provided then explain
the characteristic.
• Are there any other characteristics that the
chosen equations have in common?
• Are there any other equations which have this
characteristic?
• Can you suggest some equations (not listed)
that would also have this characteristic?
• What is it about the equation that gives it that
characteristic? (Make the link between the
properties of the equation and the look of the
graph produced.)
Step 2
Record completed workspace.
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Teaching notes
Students will often come up with unusual
characteristics such as they both go through the
fourth quadrant, or explain things in simple terms
such as the lines are parallel, rather than using
terms such as gradient. Accept all reasonable
answers but guide students to understand and use
mathematical terminology.
Some students may have multiple ways of
describing the same characteristic. Connecting
these ideas is important.
When using an interactive whiteboard –
characteristics may be written in the box using the
pens, then erased for the next group.
Equations can be typed straight onto the SMART
Notebook file by double clicking (on top of the
equal sign) and editing the text boxes.
Questions to ask
• How many groups of equations can be formed
from the new list?
• Choose one equation, how many different
groups can you put that one equation into?
Teaching notes
This could also be done as a barrier activity, where
one student thinks of a characteristic and the other
student fills in the rest of the workspace.
Remember, students are free to use any graphing
tool they like initially. As they progress through
these activities, they will rely on the tool less as
their understanding of the link between the
equations and the graphs grow.
Remind the students occasionally to check their
work using the tools provided. (GeoGebra, Math
3.0, graphics calculators, table of values or a
critical friend)
In describing characteristics, encourage students
to refer to the component of the equation that
causes this to occur.
Line graphs can be created by dragging and
rotating the blue line (with arrow heads) onto one
of the graphs. It would be helpful to click on the
blue line, hold the shift key then click on the black
graph, right click over both of them and select
grouping / group from the menu.
This will link the line to the graph, making it easier
to drag both at once.
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