Making a table and plotting points 

Definition

Unit rate is defined as a ratio in which denominator is 1. In general, a unit rate is the number of dependent variables per one independent variable.

For example − A monkey eats 8 bananas in 2 minutes

The unit rate here is the number of bananas the monkey eats in a minute.

Unit rate = 8/2 = 4 bananas per minute.

Unit rate and table

If we have a proportional relationship like for example 9for3kg,wecanmakeatableofvaluesandgraphtherelationship.Wealreadyhavelearntaboutunitrate.Inthiscasetheunitrateisthenumberofdollarsper1kg.Heretheunitrateisfoundas9/3kg = $3/kg.

In a table or graph, representing proportional relationships, the constant of proportionality and the unit rate are same.

Given a unit rate we can write pairs of x and y values following the proportional relationship as follows. For example if the unit rate is 3/kgwecanwrite(1kg,3), 2kg,$6, 3kg,$9, 4kg,$12, 5kg,$15 and so on. We then put these ordered pairs in a table as follows.

Weight in kgx	Cost in $(y)
1	3
2	6
3	9
4	12
5	15

Unit rate and graph

The proportional relationship for given rate $3/kg can be written as an equation y = 3x. The same can be plotted as a graph given below.

Given a unit rate, we can write a function rule like y = mx, where m is the unit rate, x and y are the variables. Using this rule we can find points with x and y values which can be put in a table. Then we plot these points on a graph.

Example 1

The relationship having unit rate is given by the equation: y = 2x + 1 Make a table and plot 5 points.

Solution

Step 1:

In the equation y = 2x + 1,

For x = 0, y = 1, for x = 1, y = 3 and so on

For different values of x, we get the following table

Inputx	Outputy
0	1
1	3
2	5
3	7
4	9

Step 2:

Plotting these points we get this graph

Example 2

The relationship having unit rate is given by the equation: y = 5x. Make a table and plot 5 points.

Solution

Step 1:

In the equation y = 5x

For x = 0, y = 0, for x = 1, y = 5 and so on

For different values of x, we get the following table

Inputx	Outputy
0	0
1	5
2	10
3	15
4	20

Step 2:

Plotting these points we get this graph