For two lines to be perpendicular, their slopes must satisfy the condition that the product of their slopes equals $-1$. In other words, if the slope of one line is $m_1$ and the slope of the other line is $m_2$, then:

$m_1 \times m_2 = -1$

This means that one slope must be the negative reciprocal of the other. For example:

• If one line has a slope of $2$, a line perpendicular to it would have a slope of $-\frac{1}{2}$.
• If one line has a slope of $-\frac{3}{4}$, a line perpendicular to it would have a slope of $\frac{4}{3}$.

If you're working with specific lines or slopes, I can help confirm whether they are perpendicular or not. Do you have specific lines in mind?

Would you like further clarification on perpendicularity or more examples?

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Here are 5 related questions:

1. How do you determine if two given line equations are perpendicular?
2. Can horizontal and vertical lines be considered perpendicular?
3. How does the perpendicular slope change for parallel lines?
4. What happens if one line is a constant (horizontal or vertical) and the other has a slope?
5. Can two curves have perpendicular tangents at a given point?

Tip: Perpendicularity can also be used in three dimensions, but it involves vector dot products!