The equation you provided is $-2x - 4y = 11$. Let's rearrange this into slope-intercept form $y = mx + b$ to better understand the relationship between $x$ and $y$.

Step 1: Isolate $y$

We want to isolate $y$ on one side of the equation. Begin by moving the term involving $x$ to the other side.

$-4y = 2x + 11$

Step 2: Solve for $y$

Now, divide the entire equation by $-4$ to solve for $y$.

$y = -\frac{1}{2}x - \frac{11}{4}$

This is the slope-intercept form, where the slope $m = -\frac{1}{2}$ and the y-intercept is $-\frac{11}{4}$.

Let me know if you'd like to explore further or clarify anything.

Here are 5 related questions for further practice:

1. How would you solve for $x$ in the equation $-2x - 4y = 11$?
2. What is the slope of the line from the equation $3x - 5y = 12$?
3. What are the intercepts of the equation $y = -\frac{1}{2}x - \frac{11}{4}$?
4. How would you graph the equation $-2x - 4y = 11$?
5. Can you solve $-2x - 4y = 11$ for $x$?

Tip: When converting to slope-intercept form, always aim to isolate $y$ and simplify the slope to reveal the rate of change.