Determine whether the variation model is of the form $y = k x$ or $y = \frac { k } { x }$ and find k.Then write a model that relates y and x.
$$\begin{array} { | c | c | c | c | c | c | }
\hline x & 5 & 10 & 15 & 20 & 25 \
\hline y & 26 & 13 & \frac { 26 } { 3 } & \frac { 13 } { 2 } & \frac { 26 } { 5 } \
\hline
\end{array}$$
A) $y = \frac { 130 } { x }$
B) $y = \frac { x } { 130 }$
C) $y = \frac { 1 } { x }$
D) $y = 130 x$
E) $y = x$

Question

Determine whether the variation model is of the form $y = k x$ or $y = \frac { k } { x }$ and find k.Then write a model that relates y and x. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 5 & 10 & 15 & 20 & 25 \
\hline y & 26 & 13 & \frac { 26 } { 3 } & \frac { 13 } { 2 } & \frac { 26 } { 5 } \
\hline
\end{array}$$
A) $y = \frac { 130 } { x }$
B) $y = \frac { x } { 130 }$
C) $y = \frac { 1 } { x }$
D) $y = 130 x$
E) $y = x$

Quizplus · Accepted Answer

The variation model is of the form $y = \frac { k } { x }$ because as $x$ increases, $y$ decreases, which is characteristic of an inverse variation. To find $k$, we can use any pair of $x$ and $y$ values from the table. For example, using $x = 5$ and $y = 26$, we get $26 = \frac { k } { 5 }$, which gives $k = 130$. Therefore, the model that relates $y$ and $x$ is $y = \frac { 130 } { x }$.

Determine Whether the Variation Model Is of the Form y=kxy = k xy=kx

Determine Whether the Variation Model Is of the Form $y = k x$