If $y$ varies directly as $x$ and $y=-21$ when $x=40$, find $y$ if $x=43$. (Round off your answer to the nearest hundredth.

Step 1 ：Given that $y$ varies directly as $x$, we can write this relationship as $y = kx$, where $k$ is the constant of variation.

Step 2 ：Substitute the given values of $x$ and $y$ into the equation to find $k$. We know that when $x = 40$, $y = -21$. So, $-21 = k \times 40$.

Step 3 ：Solving for $k$, we get $k = \frac{-21}{40} = -0.525$.

Step 4 ：Now that we have the value of $k$, we can find the value of $y$ when $x = 43$. Substitute these values into the equation $y = kx$ to get $y = -0.525 \times 43$.

Step 5 ：Solving for $y$, we get $y = -22.57$.

Step 6 ：Final Answer: The value of $y$ when $x=43$ is \(\boxed{-22.57}\).