Question

Suppose $y$ varies directly with $x\text{and}y=72\text{when}x=6.$ What direct variation equation relates $x$ and $y$? What is the value of $y$ when$x=10$

• A. $y=\frac{1}{12}x;120$
• B. $y=12x;120$
• C. $y=6x;62$
• D. $y=\frac{1}{6}x;43.2$

Answer 1

The correct option is B

$y=12x;120$

Explanation for the correct option:

First, we must find the constant of proportionality, $k$, shared between $y\text{and}x$. Since they're directly proportional, we have $y=kx$.

Given that $y$ is $72$ when $x$ is $6$, we can substitute these values into the equation and solve for $k$.

$$\begin{gathered} 72=6k \\ k=\frac{72}{6}=12 \end{gathered}$$

Now, since $k=12$, we can substitute this into the equation and have $y=12x$, which is the direct variation equation relating $x$ and $y$.

Now, using this equation, the value of $y$ when $xis10$ is equal to $y=12\left(10\right)=120.$

Hence, the correct answer is option (B).