Q12. - Algebra 1

Question

Solve. Assume that $\mathit{y}$ varies inversely as $\mathit{x}$.

If $\mathbf{y}\mathbf{=}\mathbf{-}\mathbf{1}$ when $\mathbf{x}\mathbf{=}\mathbf{-}\mathbf{3}$, find $\mathit{y}$ when $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{9}$.

Step-by-Step Solution

Answer

When $x=-9$, $\mathit{y}\mathbf{=}\mathbf{-}\frac{1}{3}$.

Step 1. Product rule for inverse variation.

If $(a_1,b_1)$ and $(a_2,b_2)$ are solutions of an inverse variation, then the products $a_1{b}_1$ and $a_2{b}_2$ are equal.

Step 2. Apply product rule.

Apply product rule for inverse variation.

$\begin{array}{c}{x}_1{y}_1=x_2{y}_2\\ (-3)(-1)=(-9)\left(y\right)\end{array}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{array}{c}\frac{3}{-9}=\frac{-9y}{-9}\\ y=-\frac{1}{3}\end{array}$

Therefore, when $x=-9, y=-\frac{1}{3}$.