Question

rewrite the equation in ax + by = c form. use integers for a, b, and c. y + 6 = -3(x + 4)

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(y + 6=-3(x + 4)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a=-3\), \(b = x\) and \(c = 4\), so \(-3(x + 4)=-3x-12\). The equation becomes \(y + 6=-3x-12\).

Step2: Move all terms to the left side

We want to get the equation in the form \(Ax+By = C\). So we add \(3x\) to both sides of the equation \(y + 6=-3x-12\) and subtract 6 from both sides.
Adding \(3x\) to both sides: \(3x+y + 6=-12\).
Subtracting 6 from both sides: \(3x+y=-12 - 6\).

Step3: Simplify the right side

Simplify \(-12-6=-18\). So the equation \(3x + y=-18\) is in the form \(Ax+By = C\) where \(A = 3\), \(B = 1\) and \(C=-18\).

Answer:

\(3x + y=-18\)