To express the equation $-3x + 4y - 19 = 0$ in slope-intercept form, we need to rearrange it into the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step-by-step process:

1. Start with the original equation: $-3x + 4y - 19 = 0$

2. Move the term $-3x$ to the other side: $4y = 3x + 19$

3. Divide both sides of the equation by 4 to isolate $y$: $y = \frac{3}{4}x + \frac{19}{4}$

Now, the equation is in slope-intercept form:
$y = \frac{3}{4}x + \frac{19}{4}$

The slope is $\frac{3}{4}$ and the y-intercept is $\frac{19}{4}$.

Would you like to ask more about this, or need more clarification?

Here are some questions you might explore next:

1. How can we find the x-intercept of this equation?
2. What is the significance of the slope in a linear equation?
3. How do we graph a line using the slope-intercept form?
4. How do you convert a slope-intercept form to standard form?
5. What is the relationship between the slope and parallel or perpendicular lines?

Tip: The slope $\frac{3}{4}$ indicates that for every 4 units you move horizontally, the line rises by 3 units vertically.