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3 years ago

What is y=4/5x+2 written in standard form

Mathematics

2 answers:

shepuryov [24]3 years ago

5 0

Answer:

$4x-5y=-10$

Step-by-step explanation:

we know that

The equation of the line in standard form is in the form

$Ax + By = C$

where

A is a positive integer, and B, and C are integers

In this problem we have

$y=\frac{4}{5}x+2$ ----> equation of the line in slope intercept form

Convert to standard form

Multiply by 5 both sides

$5y=4x+10$

$4x-5y=-10$

cluponka [151]3 years ago

3 0

Answer:

$4x-5y=-10$

Step-by-step explanation:

The given equation is

$y=\frac{4}{5}x+2$

Multiply through by 5.

$\Rightarrow 5y=4x+10$

Group the variable terms on the left hand side.

$\Rightarrow 5y-4x=10$

$\Rightarrow 4x-5y=-10$

The equation is now in the form: $ax+by=c$ . This is the standard form.

You might be interested in

Find three real numbers x, y, and z whose sum is 6 and the sum of whose squares is as small as possible. g

mart [117]

We're minimizing $x^2+y^2+z^2$ subject to $x+y+z=6$ . Using Lagrange multipliers, we have the Lagrangian

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(x+y+z-6)$

with partial derivatives

$\begin{cases}L_x=2x+\lambda\\L_y=2y+\lambda\\L_z=2z+\lambda\\L_\lambda=x+y+z-6\end{cases}$

Set each partial derivative equal to 0:

$\begin{cases}2x+\lambda=0\\2y+\lambda=0\\2z+\lambda=0\\x+y+z=6\end{cases}$

Subtracting the second equation from the first, we find

$2x-2y=0\implies x=y$

Similarly, we can determine that $x=z$ and $y=z$ by taking any two of the first three equations. So if $x=y=z$ determines a critical point, then

$x+y+z=3x=6\implies x=y=z=2$

So the smallest value for the sum of squares is $2^2+2^2+2^2=12$ when $(x,y,z)=(2,2,2)$ .