F4 Mathematics Direct and Inverse Proportion

F4 Mathematics

Direct and Inverse Proportion

by Karla Williamson

​Objectives

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To determine and use equations involving a constant a proportionality, for directly and inversely proportional relationships.

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In our day-to-day life, we frequently encounter situations where the variation in values of a certain quantity is influenced by the variation in values of the other quantity.

​Introduction

Direct and Inverse Proportion Class 8 | Blog

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Direct Proportion​

​Direct Proportion

​The definition of direct proportion states that "When the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease, then the two quantities are said to be in a direct proportion".

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​Can you think of any real life examples?

​Direct Proportion

​"Two quantities are in direct proportion if they both increase/decrease at the same rate. When one quantity is zero, so is the other."

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​Direct Proportion

​If two quantities, y and x, are in direct proportion to each other, we write:

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​This can also be read as 'y varies directly as x'

​Step 1: Find the Constant (k)

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y

• x

• 14

Multiple Choice

Which equation exhibits a direct proportion?

• y = 5x - 2

• y = 3/4 x

• y - x = 4

• x = 6

Multiple Choice

Which equation is not an example of direct proportion?

• y = x

• y = 3x

• y = - 6x

• y = 2/3 x + 5

Multiple Choice

What is the value of k in the following equation? y = 2/7 x

• 4

• -4

• 2/7

• 7

Multiple Choice

Upon seeing, "y varies directly as x" we immediately.....

• write down what x and y are

• write down what k is equal to

• substitute into the equation

• write y = kx

Multiple Choice

What means the same thing as direction proportion

• x = y

• direct variation

• y = k + x

• scale up proportion

Multiple Choice

Y varies directly as x. If y = 39 when x = 52, what is the best answer for k?

• k = 52

• k = 4/3

• k = 3/4

• k = 39/52

Multiple Choice

What is the direct proportion equation for the following information. x = 12, y = 16

• 16 = k(12)

• y = kx

• y = 4/3 x

• k = 16/12

​Remember, to ALWAYS write the equation linking the two variables FIRST.

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• ​Substitute the given values to find the constant.

• ​Write the linking equation.

​Finding Unknown Variables

​Once you know the value of the constant, i.e. k, AND you have written your equation linking the variables, you will be able to find unknown variables.

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​Let's look at a video. Just follow first and you will be given time to write after.

​Class work/Homework

Volume 1

Page 319

Ex. 7k

Questions 1, 6, 8, 4(a)

Multiple Choice

Y varies directly as x. If y = 12 when x = 15, what is y when x = 20?

• 4/5

• 17

• 16

• 25

Multiple Choice

n varies directly with c. If c = 24 when n = 18, what is c when n = 22?

• 88/3

• 28

• 66/4

• 24

Multiple Choice

• 10

• 2.5

• 2

• 20

Multiple Choice

• 256

• 4

• 64

• 128

Multiple Choice

• 20

• 4

• 5

• 24

Indirect Proportion​

aka Inverse Variation​

​Indirect Proportion

When the value of one quantity increases with respect to decrease in other or vice-versa, then they are said to be inversely proportional. 

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It means that the two quantities behave opposite in nature. For example, speed and time are in inverse proportion with each other. As you increase the speed, the time is reduced.

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The other terms used here for this type of proportion are inverse proportion or varying inversely or inverse variation or reciprocal proportion.

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​Can you think of any other examples?

​Class work/Homework

Volume 1

Page 319

Ex. 7k

Questions 2, 3b, 7

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