Find a line that passes through (3,5) perpendicular to a line whose slope is -1/9

miklintisyt
2022-10-15
Answered

Find a line that passes through (3,5) perpendicular to a line whose slope is -1/9

You can still ask an expert for help

RamPatWeese2w

Answered 2022-10-16
Author has **15** answers

The standardised equation of a strait line is y=mx+c where m is the gradient.

Any line perpendicular to this will have the gradient of:

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}(-1)\times \frac{1}{m}$

So in this case as $m=-\frac{1}{9}$ the gradient of the perpendicular is:

$(-1)\times -\frac{9}{1}=+9$

Thus the equation of the line we are after is y=9x+c

This line passes through the point $(x,y)\to (3,5)$

so by substitution we have:

$y=9x+c\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to \phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5=9\left(3\right)+c$

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5=27+c$

subtract 27 from both sides

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5-27=27-27+c$

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}c=-22$

Thus we have:

$y=9x-22$

Any line perpendicular to this will have the gradient of:

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}(-1)\times \frac{1}{m}$

So in this case as $m=-\frac{1}{9}$ the gradient of the perpendicular is:

$(-1)\times -\frac{9}{1}=+9$

Thus the equation of the line we are after is y=9x+c

This line passes through the point $(x,y)\to (3,5)$

so by substitution we have:

$y=9x+c\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to \phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5=9\left(3\right)+c$

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5=27+c$

subtract 27 from both sides

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}5-27=27-27+c$

$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}c=-22$

Thus we have:

$y=9x-22$

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-05-16

Suppose we have the following non-linear differential equation

$\ddot{x}+{\omega}^{2}(t)x-\frac{1}{{x}^{3}}=0$

with $x(t)$ being a real function (and $\omega (t)$ being also time-dependent).

Is there an analytical solution?

If not, is there an analytical solution for some particular form of $\omega (t)$?

If the answer is again no, what software would be recommendable for numerical solution?

$\ddot{x}+{\omega}^{2}(t)x-\frac{1}{{x}^{3}}=0$

with $x(t)$ being a real function (and $\omega (t)$ being also time-dependent).

Is there an analytical solution?

If not, is there an analytical solution for some particular form of $\omega (t)$?

If the answer is again no, what software would be recommendable for numerical solution?

asked 2022-09-28

Find the slope of a line that is perpendicular to C(13, 2), D(15, -5)

asked 2022-02-22

Usually linear regression involves two variables (x,y), i.e. an independent variable x and a dependent variable y, and they are related by the following expression

$y={a}_{0}+{a}_{1}x$

where$a}_{0$ and $a}_{1$ are parameters that define the linear model. In linear regression we have one equation of this form for each couple of observed variables $({x}_{i},{y}_{i})$ , thus we have a linear system and its solution gives us $a}_{0$ and $a}_{1$ .

Let's consider that we have two set of independent-dependent variables, namely (x,y) and (w,z). The first two variables (x,y) are related by the previous equation, while the second two variables (w,z) are related by the following

$z={b}_{0}+{b}_{1}w$

where$b}_{0$ and $b}_{1$ are parameters that define the linear relation between z and w. Also in this case a set of observation $({w}_{j},{z}_{j})$ leads to a linear system and its solution gives us $b}_{0$ and $b}_{1$ .

In general, if$a}_{0},{a}_{1$ and $b}_{1$ are independent, then we can solve the two linear systems separately. But now, let's suppose that $a}_{0$ and $b}_{0$ are independent, while $a}_{1}={b}_{1$ . In this case, the two linear systems should be solved simultaneously.

I've solved this problem just definying one linear system of equation involving both the two sets of equations, but I would like to know if this problem has a specific name and how to correctly approach it. In particular, I want to know how to assessing the fit quality (for example, with an equivalent of the$R}^{2$ ).

where

Let's consider that we have two set of independent-dependent variables, namely (x,y) and (w,z). The first two variables (x,y) are related by the previous equation, while the second two variables (w,z) are related by the following

where

In general, if

I've solved this problem just definying one linear system of equation involving both the two sets of equations, but I would like to know if this problem has a specific name and how to correctly approach it. In particular, I want to know how to assessing the fit quality (for example, with an equivalent of the

asked 2022-02-22

Transform each equation into standard form:

$a.y=2x\u20138$

$b.y=-\frac{4}{7}x+2$

$c.y-2=-5(x+1)$

$d.y+4=\frac{2}{5}(x+3)$

asked 2022-10-29

Find the slope of any line perpendicular to the line passing through (6,12) and (5,2)

asked 2022-09-27

An express train travels 80 kilometers per hour from Ironton to Wildwood. A local train, traveling at 48 kilometers per hour, takes 2 hours longer for the same trip. How far apart are Ironton and Wildwood?