Question

what is $y = \frac{2}{3}x + 4$ written in standard form? choose 1 answer: a $y - \frac{2}{3}x - 4 = 0$ b $y = \frac{2}{3}(x + 6)$ c $3y = 2x + 12$ d $-2x + 3y = 12$

Explanation:

Step1: Recall standard form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is non - negative. We start with the equation \(y=\frac{2}{3}x + 4\).

Step2: Eliminate the fraction

Multiply each term in the equation \(y=\frac{2}{3}x + 4\) by 3 to get rid of the fraction.
\(3\times y=3\times\frac{2}{3}x+3\times4\)
Simplifying each term: \(3y = 2x+12\)

Step3: Rearrange to standard form

Subtract \(2x\) from both sides of the equation \(3y = 2x + 12\).
\(- 2x+3y=12\) (or we can also write it as \(2x - 3y=- 12\), but among the given options, \(-2x + 3y = 12\) is option D)

Answer:

D. \(-2x + 3y = 12\)