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Direct Proportion

If y varies...

Question

If $y$ varies as the sum of three quantities of which the first is constant, the second varies as $x$ , and the third as $x^{2}$ ; and if $y = 0$ when $x = 1, y = 2$ when $x = 2$ , and $y = 4$ when $x = 3$ ; find $y$ when $x = 7$ .

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Solution

According to the question $y = a + b x + c x^{2}$

For $x = 1, y = 0 ⟹ a + b + c = 0 . . . (1)$

For $x = 2, y = 2 ⟹ a + 2 b + 4 c = 2 . . . (2)$

For $x = 3, y = 4 ⟹ a + 3 b + 9 c = 4 . . . (1)$

Solving (1), (2) and (3), we will get $a = - 2, b = 2$ and $c = 0$

$∴ y = - 2 + 2 x$

$⟹$ for $x = 7, y = - 2 + 2 \times 7 = 12$

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