Chapter 2 - Functions, Equations, and Graphs - 2-5 Using Linear Models - Practice and Problem-Solving Exercises - Page 98: 27

$2x-y=-2$

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{array}{l}\require{cancel} y_1=6 ,\\x_1=2 ,\\m=2 ,\end{array} is \begin{array}{l}\require{cancel} y-6=2(x-2) \end{array} In the form $Ax+By=C$ or the Standard Form of Linear Equations, the equation above is equivalent to \begin{align*} y-6&=2x-4 \\ -2x+y&=-4+6 \\ -2x+y&=2 \\ -1(-2x+y)&=(2)(-1) \\ 2x-y&=-2 .\end{align*}