Question

1. convert the equation $y - 3x = 6$ into standard form.

a. $3x + y = 6$
b. $-3x + y = 6$
c. $3x - y = -6$
d. $x - 3y = -6$

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 \(y-3x = 6\).

Step2: Rearrange the equation

Let's rewrite the equation \(y - 3x=6\) in the form \(Ax + By = C\). First, we can rewrite \(- 3x+y=6\) as \(3x - y=- 6\) (by multiplying both sides of the equation \(-3x + y=6\) by \(- 1\)). When we multiply each term in \(-3x + y = 6\) by \(-1\), we get \((-1)\times(-3x)+(-1)\times y=(-1)\times6\), which simplifies to \(3x - y=-6\).

Answer:

c. \(3x - y=-6\)