[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -\frac{4}{9} &,& \frac{4}{9}~)
% (c,d)
&&(~ \frac{6}{5} &,& \frac{4}{5}~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{\frac{4}{5}-\frac{4}{9}}{\frac{6}{5}-\left( -\frac{4}{9} \right)}\implies \cfrac{\frac{4}{5}-\frac{4}{9}}{\frac{6}{5}+\frac{4}{9}}[/tex]
[tex]\bf \cfrac{\quad \frac{36-20}{45}\quad }{\frac{54+20}{45}}\implies \cfrac{\quad\frac{16}{45} \quad }{\frac{74}{45}}\implies \cfrac{16}{45}\cdot \cfrac{45}{74}\implies \cfrac{16}{74}\implies \cfrac{8}{37}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-\cfrac{4}{9}=\cfrac{8}{37}\left[ x -\left( -\cfrac{4}{9} \right)\right][/tex]
[tex]\bf y-\cfrac{4}{9}=\cfrac{8}{37}\left( x +\cfrac{4}{9} \right)\implies y-\cfrac{4}{9}=\cfrac{8}{37}x+\cfrac{32}{333}
\\\\\\
y=\cfrac{8}{37}x+\cfrac{32}{333}+\cfrac{4}{9}\implies y=\cfrac{8}{37}x+\cfrac{32}{333}+\cfrac{148}{333}\implies y=\cfrac{8}{37}x+\cfrac{180}{333}
\\\\\\
y=\cfrac{8}{37}x+\cfrac{20}{37}\implies \stackrel{standard~form}{-\cfrac{8}{37}x+y=\cfrac{20}{37}}[/tex]
