Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

What's perpendicular to:
y= x-1

And

y= -1/3x -1

Sagot :

[tex]k:y=m_1x+b_1;\ l:y=m_2x+b_@\\\\k\ \perp\ l\iff m_1m_2=-1\\\\========================\\k:y=x-1;\ l:y=mx+b\\\\k\ \perp\ l\iff1m=-1\to m=-1\\\\l:y=-1x+b\to y=-x+b\ (b\in\mathbb{R})\\==========================\\k:y=-\frac{1}{3}x-1;\ l:y=mx+b\\\\k\ \perp\ l\iff-\frac{1}{3}m=-1\to m=3\\\\l:y=3x+b\ (b\in\mathbb{R})[/tex]
AL2006
Those are two separate lines, and they're not parallel or perpendicular
to each other.
So there's no line that's perpendicular to both of them, and you're asking
two separate questions.

For both of them, you have to remember this: 
Lines that are perpendicular have negative reciprocal slopes.

-- The slope of [ y = x - 1 ] is 1, and the negative reciprocal of 1 is -1/1 = -1 .
A line perpendicular to [ y = x - 1 ] is [ y = -x + any number ].

-- The slope of [ y = -1/3 x - 1 ] is -1/3, and the negative reciprocal of -1/3 is 3 .
A line perpendicular to [ y = -1/3 x - 1 ] is [ y = 3x + any number ].


We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.