Problem 33
Question
If two lines are parallel, describe the relationship between their slopes.
Step-by-Step Solution
Verified Answer
The slopes of two parallel lines are equal.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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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Problem 32
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