How do you find the slope of a line perpendicular to #y=7/5x-2#?

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How do you find the slope of a line perpendicular to #y=7/5x-2#?

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Answer 1 · 2015-06-20T11:32:38

The slope is #-5/7#

Explanation:

The slope of your line is #7/5#, therefore a director vector of your line is, for example, #vec{AB} (5,7)# (because the slope is #(Delta y) /(Delta x)#).

The vector #vec{u} (-7,5)# is orthogonal with #vec{AB}# because dot product is null : #5 \times(-7) + 7\times 5 = 0#.

Finally, the slope is #(Delta y) /(Delta x) = 5/-7 = - 5/7#.

Remark. You need orthonormal system for the equation of the line. But I suppose it is :-)

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How do you find the slope of a line perpendicular to #y=7/5x-2#?

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