Question

rewrite the equation in ax+by=c form. use integers for a, b, and c. y - 5 = -4(x + 4)

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(y - 5=-4(x + 4)\). Using the distributive property \(a(b + c)=ab+ac\), where \(a=-4\), \(b = x\) and \(c = 4\), we get \(y-5=-4x-16\).

Step2: Move all terms to left side

Next, we want to get the equation in the form \(Ax + By=C\). We add \(4x\) to both sides of the equation \(y-5=-4x - 16\) to get \(4x+y-5=-16\). Then we add 5 to both sides of the equation. So \(4x + y=-16 + 5\).

Step3: Simplify the constant term

Simplify the right - hand side: \(-16 + 5=-11\). So the equation in \(Ax+By = C\) form is \(4x + y=-11\).

Answer:

\(4x + y=-11\)