Ratios and Graphing
Common Core Standard: Make tables of equivalent ratios relating quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Coordinate plane – is a graph, it is the intersection of a horizontal number line and vertical number line

x –axis – this is the horizontal number line on a graph

y – axis – this is the vertical number line on a graph

Origin- this is the point where the x-axis and the y-axis intersect

Coordinates- are the locations of points on a graph

How to write coordinates?

o
Coordinates tell where a point is located they are written in a specific form
o
The x-coordinate comes first followed by a comma and the y-coordinate
o
The x-coordinate tells the location of the point along the x- axis (how far left or right the point is)
o
The y-coordinate tells the location of the point along the y-axis (how far up or down the point is)
o
Note: Coordinates are written in parenthesis
Quadrants – are the four sections of the coordinate plane
o
These are numbered from 1-4, which help to determine the value and location of points in a coordinate
plane
o
The quadrants go in a counterclockwise order and are numbered using Roman Numerals

Ratio Graphing Example: Using the ratio table below, graph the following ratios to determine the number
of defects per number of parts:

Note: When graphing, the unit rate is always the x-coordinate
Number of Parts
92
210
344
400
550
Number of
22
50
82
95
131
Defects
o
The first coordinate for this would be (92, 22), where 92 is how many the point is to the right, and 22 is
how many up the point is.
o
The following coordinates would be (210, 50), (344, 82), (400, 95), and (550, 131)
o
When graphing, it is also important to label the x and y axes, so that anyone looking at the
coordinate plane could determine what it is

o
Also, notice that ratios on a coordinate plane form a line!
o
This coordinate plane shown below includes only the first quadrant
Example: Determine the missing value from the ratio table shown below:
o
4
5
8
10
12
20
10
12.5
20
25
n
50
1st: Determine if the ratios are proportional

The first two ratios are 4:10 and 5:12.5

What does 10 ÷ 4?

10 ÷ 4 = 2.5

If 12.5 ÷5 also equals 2.5, then we know that these are proportional, since they are related by
the same quantity
o

12.5 ÷5 = 2.5, so these are proportional

This means that 8 ● 2.5 should equal 20 and it does!

10 ● 2.5 = 25

20 ● 2.5 = 50

Yes, they are proportional
2nd: Determine the unit rate

o
We know the unit rate is 1:2.5, because this is how all the ratios are related
3rd: Determine the missing number

Using the unit rate 1:2.5, we can multiply 12 by 2.5

Why? Since the 12 and 1 would be in the same position as ratios, to get from 1 to 2.5,
multiply by 2.5, so multiply 12 by 2.5

Remember the unit rate is also proportional to the ratios in the table

12 ● 2.5 = 30

Thus, n = 30