Answer :
We will investigate the specific type of relationships: Direct and inverse relations.
We will take reference of two variables as follows:
[tex]x\text{ and y}[/tex]Direct relationship:
The relationship between two variables is described as follows:
[tex]\text{If ( x ) increases then ( y ) must increase!}[/tex]The relationship is expressed as follows:
[tex]y\propto\text{ x}[/tex]Then to replace a proportionality sign we multiply a constant ( k ) as follows:
[tex]y\text{ = kx}[/tex]The above is an equation used for variables that are directly related! :)
We are given values for the variables as follows:
[tex]x\text{ = 3 , and y = -1 }[/tex]Using the data given we will determine the value of the proportionality constant ( k ) by plugging in the values of x and y given:
[tex]\begin{gathered} -1\text{ = k}\cdot3 \\ \textcolor{#FF7968}{k}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{\frac{1}{3}} \end{gathered}[/tex]The relationship is completely expressed a follows:
[tex]y\text{ = -}\frac{1}{3}\cdot x[/tex]We will use the above defined relationship to determine the value of ( y ) if ( x ) is:
[tex]\begin{gathered} \text{IF x = 9 , then:} \\ y\text{ = -}\frac{1}{3}\cdot9 \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = -3}} \end{gathered}[/tex]Answer:
The result is:
[tex]\textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = -3}}[/tex]
