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What is
y=(2)/(3)x+4 written in standard form?
Choose 1 answer:
(A)
y=(2)/(3)(x+6)
(B)
-2x+3y=12
(c)
3y=2x+12
(D)
y-(2)/(3)x-4=0

What is $y=\frac{2}{3} x+4$ written in standard form? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{2}{3}(x+6)$ $\newline$ (B) $-2 x+3 y=12$ $\newline$ (C) $3 y=2 x+12$ $\newline$ (D) $y-\frac{2}{3} x-4=0$

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Evaluate rational expressions II

Full solution

Q. What is

y=\frac{2}{3} x+4

written in standard form?

\newline

Choose

1

answer:

\newline

(A)

y=\frac{2}{3}(x+6)

\newline

(B)

-2 x+3 y=12

\newline

(C)

3 y=2 x+12

\newline

(D)

y-\frac{2}{3} x-4=0

Standard Form of Linear Equation: Understand the standard form of a linear equation. $\newline$ The standard form of a linear equation is $Ax + By = C$ , where $A$ , $B$ , and $C$ are integers, and $A$ should be non-negative.
Eliminating the Fraction: Multiply both sides of the equation $y = \frac{2}{3}x + 4$ by $3$ to eliminate the fraction. $\newline$ $3y = 2x + 12$
Rearranging the Equation: Move the term $2x$ to the left side of the equation to get all variable terms on one side and constants on the other. $\newline$ $-2x + 3y = 12$
Checking the Coefficient of $x$ : Check if the coefficient of $x$ is non-negative. $\newline$ The coefficient of $x$ is $-2$ , which is negative. However, in standard form, it is acceptable to have a negative coefficient for $x$ as long as $A$ , $B$ , and $C$ are integers. Therefore, the equation is in standard form.
Matching with Answer Choices: Compare the equation obtained with the answer choices. $\newline$ The equation $-2x + 3y = 12$ matches with choice (B).

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