Parallel lines have the same slope by definition. Let's break down the reasoning:
1. Definition of Slope: The slope of a line measures its steepness and direction. It is calculated as the rise (change in y) over the run (change in x).
2. Equation of a Line: A common way to express the equation of a line is in slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
3. Parallel Lines: By definition, parallel lines are always the same distance apart and never intersect. For two lines to maintain this property, they must have the same angle of inclination, which directly relates to having the same slope.
4. Mathematical Proof: If two lines are parallel, their slopes must be equal. To illustrate, consider two lines [tex]\( L1 \)[/tex] and [tex]\( L2 \)[/tex]:
- Line [tex]\( L1 \)[/tex]: [tex]\( y = m_1x + b_1 \)[/tex]
- Line [tex]\( L2 \)[/tex]: [tex]\( y = m_2x + b_2 \)[/tex]
For [tex]\( L1 \)[/tex] and [tex]\( L2 \)[/tex] to be parallel, their slopes [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] must be equal, hence [tex]\( m_1 = m_2 \)[/tex].
5. Conclusion: Since parallel lines have identical slopes, we can confidently conclude that the statement "Parallel lines have the same slope" is true.
Therefore, the correct answer is:
A. True
