https://file.aiquickdraw.com/mathbot/file/1727196546241j83cqigj.jpg

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.

A line passes through (1, -4) and is parallel to the line 3x - 8y + 1 = 0. Find the equation of the line.

Learn how to find the equation of a line passing through the point (1, -4) and parallel to the line 3x - 8y + 1 = 0. This solution covers key algebraic concepts such as parallel lines and the slope-intercept formula. Suitable for students in Grades 9-10.

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