Question

1. 3y + 2x + 12 = 0

Explanation:

Step1: Identify the goal (e.g., rewrite in slope - intercept form \(y = mx + b\))

We start with the equation \(3y+2x + 12=0\). Our aim is to solve for \(y\) to get it in the form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Isolate the term with \(y\)

Subtract \(2x\) and \(12\) from both sides of the equation.
\(3y+2x + 12-2x - 12=-2x - 12\)
Simplifying the left - hand side, we have \(3y=-2x - 12\)

Step3: Solve for \(y\)

Divide each term in the equation \(3y=-2x - 12\) by \(3\).
\(y=\frac{-2x}{3}-\frac{12}{3}\)
Simplifying the fractions, we get \(y =-\frac{2}{3}x-4\)

Answer:

If the goal was to rewrite in slope - intercept form, the answer is \(y =-\frac{2}{3}x - 4\)