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 form of a linear equation

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is non - negative. We start with the equation \(x=\frac{1}{4}y - 3\).

Step2: Eliminate the fraction

Multiply each term in the equation \(x=\frac{1}{4}y - 3\) by 4 to get rid of the fraction.
\(4\times x=4\times\frac{1}{4}y-4\times3\)
\(4x = y-12\)

Step3: Rearrange the equation to standard form

Subtract \(y\) from both sides of the equation \(4x = y - 12\):
\(4x-y=y - 12-y\)
\(4x - y=-12\)

Answer:

b. \(4x - y=-12\)