www.mathletics.com
Curriculum ReadyLinear Relationships
Linear Relationships
5I
SERIES TOPIC
1
Linear Relatonships
Mathletics Passport © 3P Learning
Q
Two snails have spoed the best leuce in the garden and are travelling in straight lines towards it for dinner. Slidy Sam is following the path:
2
y x
2= 
and Slippery Shelly is following the path:
2 2
y x
=  
Which leuce are they both moving towards if it is at the point where their paths cross?
G
i
v
e
t
h
i
s
a
g
o
!
Write a single sentence that describes the mathemacal meaning for these terms:You can use a small diagram/example to support your descripon.
RelaonshipLinearConnuous
This booklet extends on straight line concepts by invesgang the relaonship between points on a lineJoin these denions together to describe in a one sentence what you think is meant by a
linear relaonship
.
x
axis
y
axis
1 2 3 4 5 6 7

7

6

5

4

3

2

1 0

1

2

3

4

5

6

7 7 6 5 4 3 2 1
A BCEIJHFDG
Leuce Sam and Shelly are moving towards:
2
Linear Relatonships
Mathletics Passport © 3P Learning
5I
SERIESTOPIC
Linear Relationships
How
does it work?
For the equaon
y x
3 4= 
Gradientintercept form
A linear relaonship is an algebraic rule that forms a connuous, straight line when graphed.Let’s review the basic
linear equaon
.
(i) Write the gradient and
y
intercept for the graph of
y x
3 4= 
gradient
m
313= =++
^ h
y
intercept
b
4= 
^ h
(ii) Describe what these values mean for the graph of
y x
3 4= 
y mx b
= +
coecient of
x
(
m
) is the gradient the constant term (
b
) is the
y
interceptBefore graphing it is important to be able to extract the correct informaon from a linear equaon.the power of
x
and
y
is always
1
gradientintercept form
y x
3 4= 
:
m
3=
graph moves
3+
vercally (slopes up) for every
1+
horizontally
:
b
4= 
graph passes through the point
,0 4
^ h
or
the graph crosses the
y
axis at
4
For the equaon
y x
2= +
(i) Write the gradient and
y
intercept for the graph of
y x
2= +
gradient
1
m
11= =++
^ h
y
intercept
b
2= +
^ h
The
1
in front of the
x
is hidden
(ii) Describe what these values mean for the graph of
y x
2= +
Somemes the informaon needed can appear to be ‘hidden’.
:
m
1=
graph moves
1+
vercally (slopes up) for every
1+
horizontally
:
b
2= +
graph passes through the point
,0 2
^ h
or
the graph crosses the
y
axis at
2
y x
2= +
Equaon is another word for rule