Question

1. Determine whether x and y show a direct variation or inverse variation, or neither and fill in the blank space.

X 1.5 2.5 4 5
Y 20 12 7.5

Answer 1

$From \: the \: given \: data$

$Let \: x_{1} = 1.5, x_{2} = 2.5 , x_{3} = 4, x_{4} = 5 ,$

$and \: y_{1} = 20, y_{2} = 12, y_{3} = 7 t, y_{4} = \red{?}$

$i) \frac{x_{1}}{y_{1}} = \frac{1.5}{20} = 0.075$

$ii) \frac{x_{2}}{y_{2}} = \frac{2.5}{12} = 0.208$

$\blue{ \frac{x_{1}}{y_{1}} \neq \frac{x_{2}}{y_{2}}}$

$\therefore x \: not \: directly \:varies \: to \:y$

$Now, x_{1} \times y_{1} = 1.5 \times 20 = 30$

$x_{2} \times y_{2} = 2.5 \times 12 = 30$

$x_{3} \times y_{3} = 4 \times 7.5 = 30$

$\pink { x_{1} \times y_{1} = x_{2} \times y_{2} = x_{3} \times y_{3}}$

$\therefore \green { x \: and \: y \: show \: inverse }$

$\green{ variation}$

$Now, x_{4} \times y_{4} = 30$

$\implies 5 \times y_{4} = 30$

$\implies y_{4} = \frac{30}{5}$

$\implies y_{4} = 6$

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