To write the equation $7x + 4y = -7$ in slope-intercept form, which is $y = mx + b$, follow these steps:

1. Start with the given equation: $7x + 4y = -7$

2. Isolate the $y$-term on one side by subtracting $7x$ from both sides: $4y = -7x - 7$

3. Now, divide both sides of the equation by $4$ to solve for $y$: $y = \frac{-7x - 7}{4}$

4. Simplify the right side: $y = -\frac{7}{4}x - \frac{7}{4}$

Now, the equation is in slope-intercept form: $y = -\frac{7}{4}x - \frac{7}{4}$

Here, the slope $m = -\frac{7}{4}$ and the y-intercept $b = -\frac{7}{4}$.

Would you like more details on how this form relates to graphing?

Here are 5 related questions:

1. What does the slope represent in this equation?
2. How can you determine the y-intercept from the equation?
3. How would you find the x-intercept from this equation?
4. How can the equation be rewritten in standard form?
5. How does changing the slope affect the graph of the line?

Tip: The slope indicates how steep the line is and whether it rises or falls as $x$ increases.