Name: Direct Proportion: Introduction
Uploaded: 2019-07-19
Duration: 2 min 34 s
Description: Suppose you increase the number of books in your bag. What will happen to its weight? It will also increase. This is direct proportionality. Let us explore more about it.

Question

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$	$20$	$17$	$14$	$11$	$8$	$5$	$2$
$y$	$40$	$34$	$28$	$22$	$16$	$10$	$4$

Accepted Answer

From the given table, we have to check whether $x$ and $y$ are in direct variation. If they are then we have to find the value of the constant ratio.

$x$ $20$ $17$ $14$ $11$ $8$ $5$ $2$

$y$ $40$ $34$ $28$ $22$ $16$ $10$ $4$

Two variables $x & y$ are said to be in direct variation if the ratio between $x & y$ is a constant, i.e. $\frac{x}{y} = k$ .

So let us find the constant ratio in each case.

When $x = 20, y = 40$ then constant ratio is $\frac{x}{y} = \frac{20}{40} = \frac{1}{2}$

When $x = 17, y = 34$ then constant ratio is $\frac{x}{y} = \frac{17}{34} = \frac{1}{2}$

When $x = 14, y = 28$ then constant ratio is $\frac{x}{y} = \frac{14}{28} = \frac{1}{2}$

When $x = 11, y = 22$ then constant ratio is $\frac{x}{y} = \frac{11}{22} = \frac{1}{2}$

When $x = 8, y = 16$ then constant ratio is $\frac{x}{y} = \frac{8}{16} = \frac{1}{2}$

When $x = 5, y = 10$ then constant ratio is $\frac{x}{y} = \frac{5}{10} = \frac{1}{2}$

When $x = 2, y = 4$ then constant ratio is $\frac{x}{y} = \frac{2}{4} = \frac{1}{2}$

Here, the constant ratio is same for all values of $x$ and $y$ .

Hence, we can state that $x$ and $y$ are in direct variation.

$x$	$5$	$8$	$12$	$15$	$18$	$20$
$y$	$15$	$24$	$36$	$60$	$72$	$100$

Time period	$1$ year	$2$ years	$3$ years
Simple Interest (in $₹$ )
Compound Interest (in $₹$ )

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