Jairo Hodges
2022-11-21
Answered

Write an equation of a line parallel to y=3 passing through P(-2,4)

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Laura Fletcher

Answered 2022-11-22
Author has **22** answers

Your line, y=3 is a horizontal line passing through 3 (on the y axis). A line parallel to this one has to be again horizontal but this time passing through 4, i.e. y=4.

A somewhat more rigorous approach would be to say that the slope m of y=3 is zero so using the relationship:

$y-{y}_{0}=m(x-{x}_{0})$

you get:

y−4=0(x+2)

y=4

A somewhat more rigorous approach would be to say that the slope m of y=3 is zero so using the relationship:

$y-{y}_{0}=m(x-{x}_{0})$

you get:

y−4=0(x+2)

y=4

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Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-09-09

How to simplify $3\times (5+7)$?

asked 2022-02-23

My calculus book says the equation:

$y}^{\prime}+{x}^{2}y={y}^{2$

is not linear.

Linear equations must be of the form:

${y}^{\prime}+P\left(x\right)y=Q\left(x\right)$

Is the equation not in this form with Q(x) = 0?

is not linear.

Linear equations must be of the form:

Is the equation not in this form with Q(x) = 0?

asked 2022-02-24

I tried researching and found that I can use a system of linear equations and solve by an inverse matrix to find the cubic equation given 4 points which satisfy the function f(x) of the general form $f\left(x\right)=a{x}^{3}+b{x}^{2}+cx+d$

I can also find a cubic of the form$a{x}^{3}+d$ with no $x}^{2$ or x term from 2 points, however I was wondering how one would go about finding a full general form cubic given only the minimum and maximum.

Example minimums could be (-1,4) and (2,3)

I can also find a cubic of the form

Example minimums could be (-1,4) and (2,3)

asked 2022-02-22

In describing the solution of a system of linear equations with many solutions, why do we use a free variable as a parameter to describe the other variables in the solution? Why do we not we use a leading variable? Since by the commutative property of addition we can swap between the free and leading variables, e.g. x + y + z = x + z + y; The solution set will be essentially identical (albeit having different orders).

Definitions:

1. A parameter that is not a leading variable is referred to as a free variable.

2. A leading variable is the first variable in reduced form with a non-zero coefficient.

3. These definitions are clearest when applied to the Echelon form of a system of linear equations expressed as a Matrix.

For example:

Let S be the solution set of the system

$x+y+z=3$

$y-z=4$

Using the free variable z as the parameter

$S=\{(-2z-1,z+4,z)\mid z\in \mathbb{R}\}$.

Using the leading variable y as the parameter

$S=\{(-2y+7,y,y-4)\mid y\in \mathbb{R}\}$.

asked 2022-10-13

Write an equation of a line given (0,4) & is parallel to y=3x-7

asked 2022-02-23

a) Determine a condition under which (x, y, z) is a linear combination of [-3, 5, -3], [-9, 11, -3], [-6, 8, -3]? Your condition should take the shape of a linear equation. I have the theorem that every vector (x, y, z) in $R}^{3$ is a linear combination of $x(1,0,0)+y(0,1,0)+z(0,0,1)$.