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In which of t...

Question

In which of the following tables do $x and y$ vary directly:

$x$ $3$ $5$ $8$ $11$

$y$ $4.5$ $7.5$ $12$ $16.5$

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Solution

Finding the ratio of $x and y$ in each case

$x$ $3$ $5$ $8$ $11$

$y$ $4.5$ $7.5$ $12$ $16.5$

Let $x_{1} = 3, x_{2} = 5, x_{3} = 8, x_{4} = 11$

$y_{1} = 4.5, y_{2} = 7.5, y_{3} = 12, y_{4} = 16.5$

Finding the ratio of x and y in each case:

$\frac{x_{1}}{y_{1}} = \frac{3}{4.5} = \frac{2}{3}$

$\frac{x_{2}}{y_{2}} = \frac{5}{7.5} = \frac{2}{3}$

$\frac{x_{3}}{y_{3}} = \frac{8}{12} = \frac{2}{3}$

$\frac{x_{4}}{y_{4}} = \frac{11}{16.5} = \frac{2}{3}$

Since, $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}} = \frac{x_{3}}{y_{3}} = \frac{x_{4}}{y_{4}}$

Therefore, $x and y$ vary directly:

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