Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. 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 you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.