Write the equation y - 2 = 2(x - 3) in standard form

Keyla Koch
2022-10-11
Answered

Write the equation y - 2 = 2(x - 3) in standard form

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elulamami

Answered 2022-10-12
Author has **22** answers

Standard form of a line equation is ax+by=c

Given (y−2)=2(x−3)

y−2=2x−6

2x−y=6−2

2x−y=4 is in the standard form.

Given (y−2)=2(x−3)

y−2=2x−6

2x−y=6−2

2x−y=4 is in the standard form.

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Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-07-07

The differential equation of the form

${x}^{2}\frac{{d}^{2}y}{d{x}^{2}}+{p}_{1}\frac{dy}{dx}+{p}_{2}y=Q$ where ${p}_{1}$, ${p}_{2}$ are constants and Q the function of x is called Second order homogeneous linear equation.

How can we prove that above equation is second order homogeneous linear differential equation.And also help me to understand the significance of above equation in engineering field.

${x}^{2}\frac{{d}^{2}y}{d{x}^{2}}+{p}_{1}\frac{dy}{dx}+{p}_{2}y=Q$ where ${p}_{1}$, ${p}_{2}$ are constants and Q the function of x is called Second order homogeneous linear equation.

How can we prove that above equation is second order homogeneous linear differential equation.And also help me to understand the significance of above equation in engineering field.

asked 2022-06-09

Question: Given a system of linear equations

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?

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Holly's grandfather is 52 years older than her. In 7 years, the sum of their ages will be 70. Find Holly's present age

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Write an equation for the line perpendicular to y=2x−5 that contains (-9,6)

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Background

It is relatively easier to find a solution to a system of linear equations in the form of $A\mathbf{\text{v}}=\mathbf{\text{b}}$ 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 $\mathbb{R}$

$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\left[\begin{array}{c}2\\ 3\\ 4\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

Although it is easy to see that $a=\frac{1}{2},e=\frac{1}{3},i=\frac{1}{4}$ 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 ${P}_{2}(\mathbb{R})$, the problem of finding a basis $\beta $ such that $[{x}^{2}+x+1{]}_{\beta}=(2,3,4{)}^{T}$ can be reduced to a problem that has been stated above.

It is relatively easier to find a solution to a system of linear equations in the form of $A\mathbf{\text{v}}=\mathbf{\text{b}}$ 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 $\mathbb{R}$

$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\left[\begin{array}{c}2\\ 3\\ 4\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

Although it is easy to see that $a=\frac{1}{2},e=\frac{1}{3},i=\frac{1}{4}$ 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 ${P}_{2}(\mathbb{R})$, the problem of finding a basis $\beta $ such that $[{x}^{2}+x+1{]}_{\beta}=(2,3,4{)}^{T}$ can be reduced to a problem that has been stated above.

asked 2022-10-16

Find the slope of a line parallel and perpendicular to the line going through: (−7,−3) and (6,8)