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

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Solution

$\frac{x_{1}}{y_{1}} = \frac{20}{40} = \frac{1}{2}, \frac{x_{2}}{y_{2}} = \frac{17}{34} = \frac{1}{2}$
$\frac{x_{3}}{y_{3}} = \frac{14}{28} = \frac{1}{2}, \frac{x_{4}}{y_{4}} = \frac{11}{22} = \frac{1}{2}$
$\frac{x_{5}}{y_{5}} = \frac{8}{16} = \frac{1}{2}, \frac{x_{6}}{y_{6}} = \frac{5}{10} = \frac{1}{2}, \frac{x_{7}}{y_{7}} = \frac{2}{4} = \frac{1}{2}$
$\frac{x_{1}}{y_{1}} = \frac{y_{1}}{y_{2}} = \frac{x_{3}}{y_{3}} = \frac{x_{4}}{y_{4}} = . . . . \frac{1}{2}$
So, $x$ and $y$ are directly proportional.

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Similar questions

x

y

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

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

x	6	10	14	18	22	26	30
y	4	8	12	16	20	24	28

x	5	8	12	15	18	20
y	15	24	36	45	54	60

x

y

y = 20

x = 4

x = 6

Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

x

y

x_{1}, x_{2}

y_{1}

$x$	$3$	$x_{1}$	$x_{2}$	$10$
$y$	$72$	$120$	$192$	$y_{1}$

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