To rewrite the equation $-3y = 20x + 19$ in slope-intercept form $(y = mx + b)$, follow these steps:

1. Start with the given equation: $-3y = 20x + 19$

2. Divide both sides by $-3$ to solve for $y$: $y = \frac{20x + 19}{-3}$

3. Simplify the right side by dividing each term by $-3$: $y = \frac{20}{-3}x + \frac{19}{-3}$

4. This gives you the slope-intercept form: $y = -\frac{20}{3}x - \frac{19}{3}$

So, the equation in slope-intercept form is: $y = -\frac{20}{3}x - \frac{19}{3}$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for further practice:

1. How do you determine the slope from an equation in slope-intercept form?
2. What is the y-intercept in the equation $y = -\frac{20}{3}x - \frac{19}{3}$?
3. How do you convert an equation from standard form to slope-intercept form?
4. How do you graph a line using the slope and y-intercept?
5. What is the slope of the line parallel to $y = -\frac{20}{3}x - \frac{19}{3}$?

Tip: In the slope-intercept form $y = mx + b$, $m$ represents the slope, and $b$ is the y-intercept.