## Algebra 2 Common Core

$2x-5y=-23$
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*}\require{cancel} y_1&= 7 ,\\x_1&= 6 ,\\m&= \dfrac{2}{5} ,\end{align*} is \begin{align*}\require{cancel} y-7=\dfrac{2}{5}(x-6) \end{align*} In the form $Ax+By=C,$ the equation above is equivalent to \begin{align*} 5(y-7)&=\left( \dfrac{2}{5}(x-6) \right)5 \\\\ 5(y-7)&=2(x-6) \\ 5y-35&=2x-12 \\ -2x+5y&=-12+35 \\ -2x+5y&=23 \\ -1(-2x+5y)&=(23)(-1) \\ 2x-5y&=-23 \end{align*}