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. $$\begin{array} { | c | c | c | c | c | c | }
\hline x & 9 & 18 & 27 & 36 & 45 \
\hline y & 2 & 4 & 6 & 8 & 10 \
\hline
\end{array}$$
A) $y = \frac { 2 } { 9 } x$
B) $y = \frac { 9 } { x }$
C) $y = \frac { 2 } { 9 x }$
D) $y = \frac { 9 } { 2 x }$
E) $y = \frac { 9 } { 2 } x$

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. $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 9 & 18 & 27 & 36 & 45 \
\hline y & 2 & 4 & 6 & 8 & 10 \
\hline
\end{array}$$
A) $y = \frac { 2 } { 9 } x$
B) $y = \frac { 9 } { x }$
C) $y = \frac { 2 } { 9 x }$
D) $y = \frac { 9 } { 2 x }$
E) $y = \frac { 9 } { 2 } x$

Quizplus · Accepted Answer

The relationship between $y$ and $x$ is direct variation, as $y$ increases linearly with $x$. The constant of variation $k$ can be found by dividing $y$ by $x$ for any pair of values, for example, $k = \frac{2}{9}$ when $x = 9$ and $y = 2$. Therefore, the model is $y = \frac{2}{9}x$.

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

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