1. Determine whether x and y show a direct variation or inverse variat

1.	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 5Y 20 12 7.5
Answer» $From \: the \: given \: data$ $Let \: x_{1} = 1.5, x_{2} = 2.5 , x_{3} = 4, x_{4} = 5 ,$ $and \: y_{1} = 20, y_{2} = 12, y_{3} = 7 t, y_{4} = \red{?}$ $i) \frac{x_{1}}{y_{1}} = \frac{1.5}{20} = 0.075$ $ii) \frac{x_{2}}{y_{2}} = \frac{2.5}{12} = 0.208$ $\blue{ \frac{x_{1}}{y_{1}} \neq \frac{x_{2}}{y_{2}}}$ $\therefore x \: not \: directly \:varies \: to \:y$ $Now, x_{1} \times y_{1} = 1.5 \times 20 = 30$ $x_{2} \times y_{2} = 2.5 \times 12 = 30$ $x_{3} \times y_{3} = 4 \times 7.5 = 30$ $\pink { x_{1} \times y_{1} = x_{2} \times y_{2} = x_{3} \times y_{3}}$ $\therefore \green { x \: and \: y \: show \: inverse }$ $\green{ variation}$ $Now, x_{4} \times y_{4} = 30$ $\implies 5 \times y_{4} = 30$ $\implies y_{4} = \frac{30}{5}$ $\implies y_{4} = 6$ •••♪