keeping in mind that for the standard form of a linear equation
- all values must be integers
- the variables will be on the left-hand-side
- x cannot have a negative coefficient
[tex] \bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad
(\stackrel{x_2}{-5}~,~\stackrel{y_2}{-2})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-(-5)}{-5-2}\implies \cfrac{-2+5}{-5-2}\implies -\cfrac{3}{7}
\\\\\\ [/tex]
[tex] \bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=-\cfrac{3}{7}(x-2)\implies y+5=-\cfrac{3}{7}x+\cfrac{6}{7}
\\\\\\
y=-\cfrac{3}{7}x+\cfrac{6}{7}-5\implies y=-\cfrac{3}{7}x-\cfrac{29}{7}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7y=-3x-29}
\\\\\\
3x+\stackrel{\stackrel{B}{\downarrow }}{7}y=-29\impliedby \textit{standard form} [/tex]
