Find the variation equation for the variation statement.
-$y$ varies directly as the square of $x ; y = - \frac { 64 } { 5 }$ when $x = 8$
A) $y = \left( - \frac { 64 } { 5 } x \right) ^ { 2 }$
B) $y = - \frac { 64 } { 5 } x$
C) $y = \left( - \frac { 1 } { 5 } x \right) ^ { 2 }$
D) $y = - \frac { 1 } { 5 } x ^ { 2 }$

Question

Quizplus · Accepted Answer

The variation equation for direct variation is $y = kx^n$, where $k$ is the constant of variation and $n$ is the power of $x$. Given $y = -\frac{64}{5}$ when $x = 8$, and $y$ varies directly as the square of $x$, we find $k$ by substituting the given values into $y = kx^2$, resulting in $-\frac{64}{5} = k(8)^2$. Solving for $k$ gives $k = -\frac{1}{5}$, so 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