The equation of the line that passes through $(1, -4)$ and is parallel to the line $3x - 8y + 1 = 0$ is: $y = \frac{3}{8}x - \frac{35}{8}$ In the plot above:

• The blue dashed line represents the given line $3x - 8y + 1 = 0$.
• The red line is the parallel line that passes through the point $(1, -4)$, marked with a green cross.

Let me know if you'd like any further details or clarifications.

Here are some related questions to deepen understanding:

1. How can you find the equation of a line perpendicular to the given line instead of parallel?
2. What happens to the equation of a line when the slope changes but the point remains the same?
3. Can you express both lines in point-slope form?
4. How do you verify if two lines are parallel or perpendicular using their slopes?
5. What are other forms of linear equations besides slope-intercept and point-slope forms?

Tip: When lines are parallel, they always have the same slope but differ in their y-intercepts.