Solved on Feb 27, 2024

Find the proportional coefficient for $2Y + 4X = 0$ .

STEP 1

Assumptions
1. We are given the linear equation $2Y + 4X = 0$ .
2. We need to find the proportional coefficient, which is the coefficient that relates $Y$ to $X$ in the form $Y = kX$ , where $k$ is the proportional coefficient.

STEP 2

To find the proportional coefficient, we need to solve the equation for $Y$ in terms of $X$ .
$2Y + 4X = 0$

STEP 3

Isolate the term with $Y$ on one side of the equation by subtracting $4X$ from both sides.
$2Y = -4X$

STEP 4

Divide both sides of the equation by 2 to solve for $Y$ .
$Y = -\frac{4X}{2}$

STEP 5

Simplify the right side of the equation to find the proportional coefficient.
$Y = -2X$

STEP 6

The proportional coefficient $k$ is the factor that relates $Y$ to $X$ , which in this case is $-2$ .
The proportional coefficient for the equation $2Y + 4X = 0$ is $-2$ .
Therefore, the correct answer is a. -2.

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Find the proportional coefficient for $2Y + 4X = 0$ .

STEP 1

Assumptions
1. We are given the linear equation $2Y + 4X = 0$ .
2. We need to find the proportional coefficient, which is the coefficient that relates $Y$ to $X$ in the form $Y = kX$ , where $k$ is the proportional coefficient.

STEP 2

To find the proportional coefficient, we need to solve the equation for $Y$ in terms of $X$ .
$2Y + 4X = 0$

STEP 3

Isolate the term with $Y$ on one side of the equation by subtracting $4X$ from both sides.
$2Y = -4X$

STEP 4

Divide both sides of the equation by 2 to solve for $Y$ .
$Y = -\frac{4X}{2}$

STEP 5

Simplify the right side of the equation to find the proportional coefficient.
$Y = -2X$

STEP 6

The proportional coefficient $k$ is the factor that relates $Y$ to $X$ , which in this case is $-2$ .
The proportional coefficient for the equation $2Y + 4X = 0$ is $-2$ .
Therefore, the correct answer is a. -2.

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Find the proportional coefficient for 2Y+4X=02Y + 4X = 02Y+4X=0.

STEP 1

Assumptions1. We are given the linear equation 2Y+4X=02Y + 4X = 02Y+4X=0.2. We need to find the proportional coefficient, which is the coefficient that relates YYY to XXX in the form Y=kXY = kXY=kX, where kkk is the proportional coefficient.

STEP 2

To find the proportional coefficient, we need to solve the equation for YYY in terms of XXX.2Y+4X=02Y + 4X = 02Y+4X=0

STEP 3

Isolate the term with YYY on one side of the equation by subtracting 4X4X4X from both sides.2Y=−4X2Y = -4X2Y=−4X

STEP 4

Divide both sides of the equation by 2 to solve for YYY.Y=−4X2Y = -\frac{4X}{2}Y=−24X​

STEP 5

Simplify the right side of the equation to find the proportional coefficient.Y=−2XY = -2XY=−2X

STEP 6

The proportional coefficient kkk is the factor that relates YYY to XXX, which in this case is −2-2−2.The proportional coefficient for the equation 2Y+4X=02Y + 4X = 02Y+4X=0 is −2-2−2.Therefore, the correct answer is a. -2.

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Find the proportional coefficient for $2Y + 4X = 0$ .

Assumptions
1. We are given the linear equation $2Y + 4X = 0$ .
2. We need to find the proportional coefficient, which is the coefficient that relates $Y$ to $X$ in the form $Y = kX$ , where $k$ is the proportional coefficient.

To find the proportional coefficient, we need to solve the equation for $Y$ in terms of $X$ .
$2Y + 4X = 0$

Isolate the term with $Y$ on one side of the equation by subtracting $4X$ from both sides.
$2Y = -4X$

Divide both sides of the equation by 2 to solve for $Y$ .
$Y = -\frac{4X}{2}$

Simplify the right side of the equation to find the proportional coefficient.
$Y = -2X$

The proportional coefficient $k$ is the factor that relates $Y$ to $X$ , which in this case is $-2$ .
The proportional coefficient for the equation $2Y + 4X = 0$ is $-2$ .
Therefore, the correct answer is a. -2.