Respuesta :
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define the variation that occurs in the Question.
Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
STEP 2: Interpret the statements in the question tab
[tex]\begin{gathered} x\text{ varies inversely as y} \\ x\propto\frac{1}{y} \end{gathered}[/tex]STEP 3: Get the constant of variation
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \text{Introducing the constant, we have;} \\ x=k\times\frac{1}{y},x=\frac{k}{y} \\ By\text{ cross multiplication,} \\ x=ky \\ \text{Divide both sides by y} \\ \frac{x}{y}=k \end{gathered}[/tex]STEP 4: Use the given values to get the equation relating x and y
[tex]\begin{gathered} \frac{x}{y}=k,x=-2,y=3 \\ By\text{ substitution,} \\ \frac{-2}{3}=k \\ k=\frac{-2}{3} \\ \\ \text{The equation relating x and y will be:} \\ x=-\frac{2}{3}y \\ x=\frac{-2y}{3} \end{gathered}[/tex]Hence, the equation relating x and y is:
[tex]x=\frac{-2y}{3}[/tex]STEP 5: Find y when x=-1
[tex]\begin{gathered} x=ky \\ \text{Divide both sides by k to get the value of y} \\ y=\frac{x}{k} \\ x=-1,k=-\frac{2}{3} \\ By\text{ substitution,} \\ y=\frac{-1}{\frac{-2}{3}} \\ y=-1\div-\frac{2}{3} \\ y=-1\times\frac{-3}{2}=\frac{-1\times-3}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Hence, the value of y when x=-1 is 3/2
