Given:
[tex]\begin{gathered} y\alpha x \\ x=6,y=54 \end{gathered}[/tex]To Determine: The equation describing the relationship between y and x
Solution:
Step 1: Introduce the constant into the given variation
[tex]\begin{gathered} y=kx \\ k=\text{constant} \end{gathered}[/tex]Step 2: Substitute the given values of y and x to find the constant
[tex]\begin{gathered} y=kx,x=6,y=54 \\ k=\frac{y}{x} \\ k=\frac{54}{6} \\ k=9 \end{gathered}[/tex]Step 3: Substitute k into the equation
[tex]\begin{gathered} y=kx,k=9 \\ y=9x \end{gathered}[/tex]Hence, the equation describing the relationship between x and y is
y = 9x
