Suppose $x$ and $y$ vary together such that $4 x+7 y=17$. What is the constant rate of change of $y$ with respect to $x$ ? 7 $-0.5714$ 1.8571 4 13

Step 1 ：The question is asking for the rate of change of $y$ with respect to $x$. This is essentially asking for the derivative of $y$ with respect to $x$. We can find this by rearranging the equation to solve for $y$ and then taking the derivative of the resulting equation with respect to $x$.

Step 2 ：Rearrange the equation $4x + 7y = 17$ to solve for $y$ to get $y = \frac{17}{7} - \frac{4x}{7}$.

Step 3 ：Take the derivative of $y$ with respect to $x$ to get $\frac{dy}{dx} = -\frac{4}{7}$.

Step 4 ：Final Answer: The constant rate of change of $y$ with respect to $x$ is \(\boxed{-\frac{4}{7}}\).