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. $$\begin{array} { | c | c | c | c | c | c | }
\hline x & 5 & 10 & 15 & 20 & 25 \
\hline y & - 1.5 & - 3 & - 4.5 & - 6 & - 7.5 \
\hline
\end{array}$$
A) $y = - \frac { 3 } { 10 x }$
B) $y = \frac { 10 } { 3 } x$
C) $y = - \frac { 3 } { 10 } x$
D) $y = \frac { 3 } { 10 } x$
E) $y = - \frac { 10 } { 3 } x$

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. $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 5 & 10 & 15 & 20 & 25 \
\hline y & - 1.5 & - 3 & - 4.5 & - 6 & - 7.5 \
\hline
\end{array}$$
A) $y = - \frac { 3 } { 10 x }$
B) $y = \frac { 10 } { 3 } x$
C) $y = - \frac { 3 } { 10 } x$
D) $y = \frac { 3 } { 10 } x$
E) $y = - \frac { 10 } { 3 } x$

Quizplus · Accepted Answer

The relationship between $x$ and $y$ is linear, as doubling $x$ also doubles $y$, indicating a direct variation ($y = kx$). The constant $k$ can be found by dividing $y$ by $x$ for any pair of values, for example, $-1.5 / 5 = -0.3$, so $k = -\frac{3}{10}$, making the model $y = -\frac{3}{10}x$.

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

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