After determining whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ ,find the value of k.
$$\begin{array} { | c | c | c | c | c | c | }
\hline x & 20 & 40 & 60 & 80 & 100 \
\hline y & \frac { 1 } { 30 } & \frac { 1 } { 60 } & \frac { 1 } { 90 } & \frac { 1 } { 120 } & \frac { 1 } { 150 } \
\hline
\end{array}$$
A) $k = \frac { 1 } { 20 }$
B) $k = \frac { 3 } { 2 }$
C) $k = \frac { 5 } { 4 }$
D) $k = \frac { 1 } { 10 }$
E) $k = \frac { 2 } { 3 }$

Question

After determining whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ ,find the value of k. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 20 & 40 & 60 & 80 & 100 \
\hline y & \frac { 1 } { 30 } & \frac { 1 } { 60 } & \frac { 1 } { 90 } & \frac { 1 } { 120 } & \frac { 1 } { 150 } \
\hline
\end{array}$$
A) $k = \frac { 1 } { 20 }$
B) $k = \frac { 3 } { 2 }$
C) $k = \frac { 5 } { 4 }$ 
D) $k = \frac { 1 } { 10 }$
E) $k = \frac { 2 } { 3 }$

Quizplus · Accepted Answer

The variation model is of the form $y = \frac { k } { x }$ because as $x$ increases, $y$ decreases proportionally. To find $k$, use any pair of $x$ and $y$ values. For example, using $x = 20$ and $y = \frac{1}{30}$, we get $\frac{1}{30} = \frac{k}{20}$. Solving for $k$ gives $k = \frac{20}{30} = \frac{2}{3}$.

After Determining Whether the Variation Model Below Is of the Form