The graph shows the number of matchsticks m in pattern number n'

1
By the end of the PowerPoint you should be able
to answer this question
The graph shows the number of matchsticks m in
pattern number n. (a) Mark the point which shows
the number of matchsticks used in Pattern number
4.
(1)
(b) How many matchsticks are used in Pattern
number 10? (1) (c) Write down a
formula for m in terms of n. . (2) (
Total 4 marks)
2
Straight lines
22 November 2009
Learning objectives To be able to calculate the
equation of a straight line
Plot this set of data as a scatter
diagram X-axis 50 to 90 Y-axis 120 to 200
3
Draw a line of best fit
So what are the things we can investigate with a
straight line
Discuss correllation
Extrapolate
Find the equation of a straight line
4
Draw a line of best fit
A line that is drawn on a scatter graph to show
the correllation. A line that best represents
the overall pattern of the data values.
5
Draw a line of best fit
6
Discuss correllation
Correllation is a way of describing the pattern.
Here are the different types of correllation
Strong
Weak
Positive Correllation
7
Discuss correllation
Correllation is a way of describing the pattern.
Here are the different types of correllation
Strong
Weak
Negative Correllation
8
Discuss correllation
Correllation is a way of describing the pattern.
Here are the different types of correllation
No Correllation
9
Positive Correllation
Negative Correllation
Key facts about correllation
No Correllation
10
Discuss correllation
What type of correllation does this graph exhibit?
Strong Positive Correllation
11
Extrapolate
Extrapolate means to use a set of data to predict
values beyond a given range, e.g. to use a babys
weight at 3 months, 6 months and 9 months to
predict its weight at 12 months.
12
Extrapolate
210
What is the approximate height of someone who
weighs 90kg?
Use the line of best fit to approximate this value
13
Equation of a straight line
14
Equation of a straight line
Equation of a straight line always comes in the
form y m x c
Y- intercept (point where the line crosses the
y-axis)
Gradient (steepness of the line)
15
Gradient of a straight line
Gradient
Choose two points on the line where you can
easily identify the co-ordinates of those points.
For example, if the points were (2, 5) and (6,
13)
The difference between the two y values
Gradient Change in y Change
in x
The difference between the two x values
Gradient 8
2
4
16
Gradient of a straight line
2.5
Gradient Change in y Change
in x
50
20
(70, 160)
(50, 110)
17
Y-intercept of a straight line
The gradient of 2.5, means every time we go
across 1 we move up 2.5. So to get back to 0 from
50 on the x-axis, we need to move left 50 which
will mean a drop of 50 x 2.5 from 110.
Why is the y-intercept not 110?
110 (50 x 2.5)
Look at these co-ordinates, the y-intercept would
have 0 has the x co-ordinate, in otherwords (0,
.)
110 (125) -15
Y-intercept is therefore -15
Equation of this straight line is y m x c
We need to move 50 units on the x-axis to get to
the point where the x co-ordinate would be 0.
(50, 110)
y 2.5 x - 15
18
Your turn!
Try and work out the equation of this straight
line
Here is a helping hint
Gradient Change in y Change
in x
15
4.29
3.5
(3.5, 20)
Y-intercept 5
y m x c
4.29
5
(0, 5)
19
By the end of the PowerPoint you should be able
to answer this question
The graph shows the number of matchsticks m in
pattern number n.
(1)
(a) Mark the point which shows the number of
matchsticks used in Pattern number 4.
(a) Mark the point which shows the number of
matchsticks used in Pattern number 4.

• How many matchsticks are used in Pattern number
  10?

• How many matchsticks are used in Pattern number
  10?

In pattern 1 there are 6
1 x 6 6 .
In pattern 2 there are 12
2 x 6 12
In pattern 3 there are 18
3 x 6 18
So in pattern 10 there are
10 x 6 60
60
(1) (2) (Total 4 marks)
(c) Write down a formula for m in terms of
n. .
(c) Write down a formula for m in terms of
n. .
m
n
y m x c
12 6 .
Gradient Change in y Change in x
6 1
6
2 1
m
n
6
0
y m x c