# Question Video: Finding the Slope of a Straight Line given the Slope of a Perpendicular Line Mathematics • 11th Grade

If line π΄π΅ β₯ line πΆπ· and the slope of line π΄π΅ = 2/5, find the slope of line πΆπ·.

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### Video Transcript

If line π΄π΅ is perpendicular to line πΆπ· and the slope of line π΄π΅ equals two-fifths, find the slope of line πΆπ·.

Here, we are told that we have two perpendicular lines π΄π΅ and πΆπ·. Knowing that two lines are perpendicular means that we know something about the relationship between their slopes. If we define line π΄π΅ to have a slope of π sub one and line πΆπ· to have a slope of π sub two, then we know that π sub two is equal to negative one over π sub one. Given that the slope π sub one of line π΄π΅ is two-fifths, then π sub two is equal to negative one over two-fifths. This simplifies to negative five over two. Because these two lines are perpendicular, their slopes will be the negative reciprocal of one another. And so the slope of line πΆπ· is negative five over two.