Find the variation equation for the variation statement.
-$y$ varies directly as the square of $x ; y = - \frac { 81 } { 5 }$ when $x = 9$
A) $y = \left( - \frac { 1 } { 5 } x \right) ^ { 2 }$
B) $y = - \frac { 81 } { 5 } x$
C) $y = - \frac { 1 } { 5 } x ^ { 2 }$
D) $y = \left( - \frac { 81 } { 5 } x \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

The variation equation for direct variation as the square of $x$ is $y = kx^2$. Given $y = -\frac{81}{5}$ when $x = 9$, we find $k$ by substituting these values: $-\frac{81}{5} = k(9)^2$, solving for $k$ gives $k = -\frac{1}{5}$. Thus, the equation is $y = -\frac{1}{5}x^2$.

Find the Variation Equation for the Variation Statement yyy Varies Directly as the Square Of

Find the Variation Equation for the Variation Statement $y$ Varies Directly as the Square Of