Question

The value of y varies directly with x. When y-25, x 4. Answer the following questions: 1. Write the direct variation formula: 2. Plug-in the values in the formula: 3. What is the value of the constant of proportionality, k? 4. What is the value of y when x is 3? Show all your work.

Answer 1

1) The direct variation formula is:

`y=kx`

2)If y=25 and x=4, then:

`25=4\cdot k`

3) The value of the constant of proportionality is:

`\begin{gathered} 4k=25 \\ \Rightarrow k=(25)/(4) \end{gathered}`

4)If x=3, then we have the following:

`\begin{gathered} y=(25)/(4)x \\ x=3 \\ \Rightarrow y=(25)/(4)\cdot3=(75)/(4) \\ y=(75)/(4) \end{gathered}`

therefore, if x=3, then y=75/4