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

Standard Form of Linear Equation: Understand the standard form of a linear equation. 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 = (2/3)x + 4 by 3 to eliminate the fraction. 3y = 2x + 12Rearranging 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. -2x + 3y = 12Checking the Coefficient of x: Check if the coefficient of x is non-negative. 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. The equation -2x + 3y = 12 matches with choice (B).

Home

Math Problems

Algebra 2

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).