Chapter 2 - Functions, Equations, and Graphs - Mid-Chapter Quiz - Page 89: 13

$3x-y=-14$

Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions, \begin{align*} y_1=2 ,\\x_1=-4 ,\\m=3 ,\end{align*} is \begin{align*} y-2&=3(x-(-4)) \\ y-2&=3(x+4) .\end{align*} In the form $Ax+By=C,$ where $A,$ $B,$ and $C$ are integers, the equation above is equivalent to \begin{align*} y-2&=3x+12 \\ -3x+y&=12+2 \\ -3x+y&=14 \\ -1(-3x+y)&=(14)(-1) \\ 3x-y&=-14 .\end{align*}