Parallel Intersecting 9A727C

1. **Stating the problem:** We want to understand the difference between parallel lines and intersecting lines. 2. **Definition of parallel lines:** Parallel lines are two lines in the same plane that never meet, no matter how far they are extended. They have the same slope. 3. **Formula for parallel lines:** If two lines have equations $y = m_1x + b_1$ and $y = m_2x + b_2$, they are parallel if and only if $m_1 = m_2$ and $b_1 \neq b_2$. 4. **Definition of intersecting lines:** Intersecting lines are two lines that cross each other at exactly one point. 5. **Condition for intersecting lines:** Two lines intersect if their slopes are different, i.e., $m_1 \neq m_2$. 6. **Example:** Consider lines $y = 2x + 3$ and $y = 2x - 4$. Since both have slope $2$, they are parallel and never intersect. 7. **Example:** Consider lines $y = 2x + 3$ and $y = -x + 1$. Since slopes $2$ and $-1$ are different, these lines intersect at one point. 8. **Summary:** Parallel lines have equal slopes and never meet. Intersecting lines have different slopes and cross at one point.