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Chapter 1: Problem 33

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

Short Answer

Expert verified
The slopes of two parallel lines are equal.

Step by step solution

01

Understanding Parallel lines

Parallel lines are two lines in the same plane that never intersect. In terms of a coordinate plane, parallel lines will constantly maintain the same distance apart from each other.
02

Identifying the relationship

The relationship between the slopes of two parallel lines is that they are equal. This is because the slope of a line defines its steepness. So, in order for two lines to not intersect and maintain a constant distance apart, they must have the same steepness or, in other words, the same slope.
03

Formulating the relationship

Therefore, if two lines are parallel, let's say line A and line B, and the slope of line A is \( m_1 \) and the slope of line B is \( m_2 \), then \( m_1 = m_2 \).

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