Write a direct variation equation, y = kx, that satisfies the ordered pairs in the table.
-$\begin{array} { c | c | c | c | c }
\mathrm { x } & - 5 & 3 & 6 & 12 \
\hline \mathrm { y } & \frac { 5 } { 4 } & - \frac { 3 } { 4 } & - \frac { 3 } { 2 } & - 3
\end{array}$
A) $y = - \frac { 1 } { 4 } x$
B)y = -4x
C) $y = \frac { 1 } { 2 } x$
D)y = 2x

Question

Write a direct variation equation, y = kx, that satisfies the ordered pairs in the table.
-$\begin{array} { c | c | c | c | c } 
\mathrm { x } & - 5 & 3 & 6 & 12 \
\hline \mathrm { y } & \frac { 5 } { 4 } & - \frac { 3 } { 4 } & - \frac { 3 } { 2 } & - 3
\end{array}$
A) $y = - \frac { 1 } { 4 } x$
B)y = -4x
C) $y = \frac { 1 } { 2 } x$
D)y = 2x

Quizplus · Accepted Answer

To find the constant of variation $k$, we can use any pair of $x$ and $y$ values from the table. Using the first pair $(-5, \frac{5}{4})$, we can set up the equation $\frac{5}{4} = k(-5)$. Solving for $k$, we get $k = -\frac{1}{4}$. Thus, the direct variation equation is $y = -\frac{1}{4}x$.

Write a Direct Variation Equation, Y = Kx, That Satisfies