Let's zoom in on one corner of the coordinate
plane. (This corner is called the first quadrant.)

The point where the two
axes cross has a special
name: it is called the
origin.

The blue lines will help
us find points. When you
make your own graphs,
you can use the lines on
your graph paper to help
you.
(0,0)
Finding Points in the Plane



We can find every point in the plane using two
numbers. These numbers are called coordinates.
We write a point's coordinates inside
parentheses, separated by a comma, like this:
(5, 6). Sometimes coordinates written this way are
called an ordered pair.
The first number in an ordered pair is called the xcoordinate. The x-coordinate tells us how far the
point is along the x-axis.
The second number is called the y-coordinate.
The y-coordinate tells us how far the point is
along the y-axis.
Estimating Points


Sometimes, the point you
want to graph is in
between points that are
marked on the axes.
When this happens, you
must estimate where to
put your point.
For example, graph
(5, 13) using these axes:
(5,13)
Some Rules for All Graphs
 All
of your graphs should have…
A
title
At the top of the graph and underlined
 It should represent what you are
graphing (use your variables)

Some Rules for All Graphs con’t
 Labeled
Axis
Use a straight-edge to draw all lines
 Use the blue lines that are provided
for you on the graph paper.
 Axes should be drawn a few lines in
and up from the edge of the paper
 You must state what is represented
on the x-axis and what is represented
on the y-axis; include units when
necessary

Some Rules for All Graphs con’t
 The appropriate scale
 We need the graph to fill up the most
paper. To find the right scale, we divide
the range of the values by the number of
tick marks on that axis. (Range is the
highest value – the lowest value).
Then we round to a number that is easy to
count by.
How to Graph




Hold the graph paper
the tall way.
Title it using the
variables.
Label the axes; don’t
forget to include units.
Draw axes a couple of
lines up and over
Count the number of
lines going across the
x-axis starting at the
zero mark
 20 lines
Distance vs. Time
Distance (m)

Time (min)
Scale the x-axis




Find your range for the x-axis
(in science it’s the highest
data point because we
always start from zero)
Time: 10-0=10 so range is 10
Divide the range of the x-axis
by the # of lines on the x-axis:
10/20=0.5
0.5 is an easy-to-count by
number so count EVERY blue
line as 0.5
Time
(min)
0
1
2
3
4
5
6
7
8
9
10
Distance
(m)
Scale the x-axis:
Distance (m)
Distance vs. Time
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Scale the y-axis


Repeat for the y-axis: tic
marks = 30 lines
Range = 110/30=3.6667
so round to 5; Count the
y-axis by 5s
 Could also count by 4s
Time (min)
Distance
(m)
0
1
2
0
10
40
3
4
5
6
35
50
65
70
7
8
9
90
85
100
10
110
Nice Counting Numbers

Decimals:

Whole Numbers:
0.1
0.2
0.25
0.5
Once in a while you
might have to
count by a different
not so nice number!
1
2
5
10
15
20
25
50
100
Etc.
Make Ordered Pairs
(0,0)
Plot data
 (1,10)
 (2,40)
 (3,35)
 (4,50)
 (5,65)
 (6,70)
 (7,90)
 (8,85)
 (9,100)
 (10,110)
Relationship: The average
distanced traveled is fairly
constant for each time
period.
Distance vs. Time
Distance (m)

140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Review:
All Graphs need:

A title

At the top and
underlined
 Labeled
Axes
 Axes scaled
appropriately (every
tick mark increases by the
same amount; each axes
can be scaled differently)
Some Graphs need:

A Key (when necessary) If you are
putting more than one line on a graph, it
must have a key to distinguish the
difference
Different Types of
Graphs
Tables, charts and graphs are
convenient ways to clearly
show your data.
There are three basic graph forms.
Line Graph
Bar Graph
Circle (or Pie) Graph
Notice on the next few slides how each of
the following examples are used to illustrate
the data.
Choose the best graph form to express
your results.
Bar Graph
A bar graph is used to show relationships
between groups.
Chocolate Milk Sold
 The two items being
compared do not need
to affect each other.
 It's a fast way to
show big differences.
Notice how easy it is
to read a bar graph.

120
112
Amount Sold
100
80
76
72
60
53
40
33
20
0
Monday
Monday
Wednesday
Friday
Tuesday
Tuesday
Thursday
Wednesday
Day
Thursday
Friday
Circle Graph or Pie Graph


A circle graph is
used to show how
a part of
something relates
to the whole.
This kind of graph
is needed to show
percentages
effectively.
Chocolate Milk Sold
Monday
Tuesday
Wednesday
Thursday
Friday
Line Graph

A line graph is
used to show
continuing data;
how one thing is
affected by
another.
It's clear to see
how things are
going by the
rises and falls a
line graph
shows.
Chocolate MIlk Sold
120
100
Amount Sold

80
60
40
20
0
Monday
Tuesday
Wednesday
Day
Chocolate
Thursday
Friday
Chocolate Milk Sold
120
The same data
displayed in 3
different types of
graphs.
Bar Graph
112
80
76
72
60
53
40
33
20
Line Graph
Chocolate MIlk Sold
0
Monday
Monday
Wednesday
Friday
Tuesday
Tuesday
Thursday
Wednesday
Thursday
Friday
120
Day
100
Chocolate Milk Sold
Circle (Pie) Graph
Amount Sold
Amount Sold
100
80
60
40
Monday
Tuesday
20
Wednesday
Thursday
Friday
0
Monday
Tuesday
Wednesday
Day
Chocolate
Thursday
Friday
Choosing the Right Graph

Use a bar graph if you are not looking for trends (or
patterns) over time; and the items (or categories) are
not parts of a whole.
 Use a pie chart if you need to compare different
parts of a whole, there is no time involved and
there are not too many items (or categories).
 Use a line graph if you need to see how a
quantity has changed over time. Line graphs
enable us to find trends (or patterns) over time.
More Examples of
Different Graphs
Circle Graph

Used to
show how
the parts
relate to the
whole
Bar Graph
60
Column 1
50
40
30
20
10
nt
s
a
Co
u
ra
m
M
at
h
D
pu
St
te
ud
r
en
tC
ou
nc
il
0
om

Memberships in afterschool clubs
70
C

A bar graph
contains horizontal
or vertical bars.
A good way to
compare data that
can be grouped into
a category.
The bars do not
touch.
Number of Students

Clubs after school
Histograms




Special type of bar
graph
Compares different
intervals of data
rather than categories
The ranges used for
the intervals must be
the same size
Bars should touch
Line Graphs



Drawn dot-to-dot
Shows trends
To compare trends
between two or more
things, you plot
different lines for
each and include a
key

A scatter plot is
a graph made by
plotting ordered
pairs in a
coordinate plane
to show the
correlation
between two
sets of data.
y-variable
Scatter Plot
x-variable
How do you determine the best-fit
line through data points?
y-variable
Try to get an even
number of data
points on the line
and on each side
of the ruler
x-variable
Positive Correlation

A scatter plot
describes a positive
trend if, as one set
of values increases,
the other set tends
to increase.
Negative Correlation

A scatter plot
describes a negative
trend if, as one set of
values increases, the
other set tends to
decrease.
No Trend

A scatter plot shows
no trend if the
ordered pairs show
no correlation