To rewrite the equation $4x - 19y = 1$ in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, follow these steps:

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

2. Isolate $y$ on one side. First, subtract $4x$ from both sides: $-19y = -4x + 1$

3. Now, divide every term by $-19$ to solve for $y$: $y = \frac{4}{19}x - \frac{1}{19}$

So, the slope-intercept form of the equation is: $y = \frac{4}{19}x - \frac{1}{19}$

Would you like further clarification or more details on this?

Here are 5 related questions for further exploration:

1. What is the slope of the line in the given equation?
2. What is the y-intercept of the line in this equation?
3. How do you find the x-intercept from the slope-intercept form?
4. How would you graph this line using the slope and y-intercept?
5. How can you convert a slope-intercept equation back into standard form?

Tip: When rewriting in slope-intercept form, always aim to isolate $y$ on one side.