1. Let's state the problem: We want to understand the properties of two parallel lines, say $l_1$ and $l_2$, especially focusing on their gradients (slopes). 2. By definition, two lines are parallel if they never intersect, no matter how far they are extended. 3. A key property of parallel lines in the coordinate plane is that they have the same gradient (slope). This means if the gradient of $l_1$ is $m_1$ and the gradient of $l_2$ is $m_2$, then: $$m_1 = m_2$$ 4. This equality of gradients ensures the lines are always the same angle relative to the x-axis and thus never meet. 5. Another important point is that while the gradients are equal, the y-intercepts of the lines are different, so the lines are distinct and do not coincide. 6. For example, if $l_1$ has equation $y = 2x + 3$ and $l_2$ has equation $y = 2x - 4$, both have gradient $2$, so they are parallel. 7. Summary: Parallel lines have equal gradients but different y-intercepts. Final answer: Two lines $l_1$ and $l_2$ are parallel if and only if their gradients are equal, i.e., $m_1 = m_2$.