Final answer:
The student is asked to find the distance between two parallel lines represented by given equations. The process involves simplifying the equations, selecting a point on one line, and utilizing the point-to-line distance formula to find the distance between them.
Step-by-step explanation:
The question asks to find the distance between two parallel lines. It's evident that the two equations given, 3x - 4y = -7 and 6x - 8y = -1, represent lines that are parallel because they can be simplified to have the same slope. To find the distance between two parallel lines, we can use the formula for the distance of a point to a line and apply it to any point on one line and the parallel line itself.
Step-by-Step Solution:
- Simplify the equations to the same form, if necessary, to identify a common point.
- Choose any point on one of the lines, say (x1, y1).
- Use the distance from a point to a line formula to find the perpendicular distance from the chosen point to the other line. This is the distance between the two parallel lines.
By following these steps with the given equations, the distance can be determined, which represents how far apart the lines are from one another.