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Chapter 2: Problem 87

If two lines are parallel, describe the relationship between their slopes.

Short Answer

Expert verified
The slopes of two parallel lines are always equal.

Step by step solution

01

Understanding Parallel lines

Parallel lines are two lines in a plane that do not intersect or touch each other at any point. They are always the same distance apart.
02

Concept of Slope

The slope of a line, often represented by the letter 'm', can be defined as the rate at which y changes as x changes in a given line. It is usually calculated as 'rise over run' which means the ratio of the vertical change to the horizontal change.
03

Relationship between slopes of Parallel lines

The slopes of two parallel lines are always equal. If two lines are parallel, and their slopes are m1 and m2, then \( m1 = m2 \). This is due to the fact that parallel lines have the same steepness and they run in the same direction.

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