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:

$\begin{gathered} 4k=25 \\ \Rightarrow k=\frac{25}{4} \end{gathered}$

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

$\begin{gathered} y=\frac{25}{4}x \\ x=3 \\ \Rightarrow y=\frac{25}{4}\cdot3=\frac{75}{4} \\ y=\frac{75}{4} \end{gathered}$

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