Question

1. how can ( x = \frac{1}{4}y - 3 ) be rewritten in standard form?

a. ( x - \frac{1}{4}y = -3 )
b. ( 4x - y = -12 )
c. ( 4x + y = -12 )
d. ( x + 4y = -3 )

Explanation:

Step1: Recall standard line form

The standard form of a linear equation is $Ax + By = C$, where $A$, $B$, $C$ are integers, and $A\geq0$.

Step2: Eliminate the fraction

Multiply all terms by 4:
$$4\times x = 4\times\frac{1}{4}y - 4\times3$$
$$4x = y - 12$$

Step3: Rearrange to standard form

Subtract $y$ from both sides:
$$4x - y = -12$$

Answer:

b. $4x - y = -12$