Question

Direct VariationIntroduction to FunctionsAcellusIf the value of "y" varies directly with "x"and y = -1 when x = 3, find "y" if x = 9.Enter the number that belongs in the green box.y = [?]

Answer 1

We will investigate the specific type of relationships: Direct and inverse relations.

We will take reference of two variables as follows:

`x\text{ and y}`

Direct relationship:

The relationship between two variables is described as follows:

`\text{If ( x ) increases then ( y ) must increase!}`

The relationship is expressed as follows:

`y\propto\text{ x}`

Then to replace a proportionality sign we multiply a constant ( k ) as follows:

`y\text{ = kx}`

The above is an equation used for variables that are directly related! :)

We are given values for the variables as follows:

`x\text{ = 3 , and y = -1 }`

Using the data given we will determine the value of the proportionality constant ( k ) by plugging in the values of x and y given:

`\begin{gathered} -1\text{ = k}\cdot3 \\ \textcolor{#FF7968}{k}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{(1)/(3)} \end{gathered}`

The relationship is completely expressed a follows:

`y\text{ = -}(1)/(3)\cdot x`

We will use the above defined relationship to determine the value of ( y ) if ( x ) is:

`\begin{gathered} \text{IF x = 9 , then:} \\ y\text{ = -}(1)/(3)\cdot9 \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = -3}} \end{gathered}`

Answer:

The result is:

`\textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = -3}}`