Find the slope that is perpendicular to the line 2x−7y=−12

dannigurl21ck2 2022-11-21 Answered
Find the slope that is perpendicular to the line 2x−7y=−12
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Answers (1)

Cullen Petersen
Answered 2022-11-22 Author has 13 answers
First put the equation in slope-intercept form y=mx+b:
Add −2x to both sides: −7y=−2x−12
Divide everything by - 7 : y = 2 7 x + 12 7
The slope of the given line is 2 7
The slope of the perpendicular line is the negative reciprocal of the given line: - 7 2
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It is relatively easier to find a solution to a system of linear equations in the form of A v = b given the matrix A. But what systematic ways are there that allows us to obtain a matrix given a equation?
For example, consider the following equations with all terms existing in R
[ a b c d e f g h i ] [ 2 3 4 ] = [ 1 1 1 ]
Although it is easy to see that a = 1 2 , e = 1 3 , i = 1 4 with all other terms being 0 is a viable solution, I am curious if there is a more systematic way of finding a matrix that satisfies a equation. Even more importantly, how should these methods be adapted when there are added constraints on the properties of the matrix? For example, if we require that the matrix of interest should be invertible, or of rank = k?
Why I am interested in such question
Consider the vector space P 2 ( R ) , the problem of finding a basis β such that [ x 2 + x + 1 ] β = ( 2 , 3 , 4 ) T can be reduced to a problem that has been stated above.