**Constant of Proportionality :**

In this section, we will learn about constant of proportionality.

The value of the constant of proportionality is depending on the type of proportion we have between the two quantities.

There are two types of proportion:

1. Direct proportion

2. Inverse proportion

If y is directly proportional to x, then we have

where k is the constant of proportionality.

where k is the constant of proportionality.

If two different quantities are given, how to check whether the relationship between them is proportional ?

We have to get ratio of the two quantities for all the given values.

If all the ratios are equal, then the relationship is proportional.

If all the ratios are not equal, then the relationship is not proportional.

**Example 1 :**

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

**Solution : **

Let us get the ratio of x and y for all the given values.

4 / 48 = 1 / 12

7 / 84 = 1 / 12

10 / 120 = 1 / 12

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx

Substitute 4 for x and 48 for y.

48 = k(4)

12 = k

So, the constant of proportionality is 12.

**Example 2 :**

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

**Solution : **

Let us get the ratio of x and y for all the given values.

1 / 100 = 1 / 100

3 / 300 = 1 / 100

5 / 550 = 1 / 110

6 / 600 = 1 / 100

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

**Example 3 :**

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

**Solution : **

Find the ratio of x and y for all the given values.

2 / 1 = 2

4 / 2 = 2

8 / 4 = 2

10 / 5 = 2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore, the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx

Substitute 2 for x and 1 for y.

1 = k(2)

1 / 2 = k

So, the constant of proportionality is 1/2.

**Example 4 :**

**Solution : **

Find the ratio of x and y for all the given values.

1 / 2 = 1 / 2

2 / 4 = 1 / 2

3 / 6 = 1 / 2

4 / 6 = 2 / 3

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

**Example 5 :**

**Solution : **

Find the ratio of x and y for all the given values.

1 / 23 = 1 / 23

2 / 36 = 1 / 18

5 / 75 = 1 / 15

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

**Example 6 :**

**Solution : **

Find the ratio of x and y for all the given values.

2 / 4 = 1 / 2

4 / 8 = 1 / 2

6 / 12 = 1 / 2

8 / 16 = 1 / 2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx

Substitute 2 for x and 4 for y.

4 = k(2)

2 = k

So, the constant of proportionality is 2.

After having gone through the stuff given above, we hope that the students would have understood constant of proportionality.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...