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A line equation in slope-intercept form is
[tex]y=mx+b[/tex]Then, to rewrite our equation in slope intercept form we just need to "isolate" the y variable on the left side of the equation.
Our line is
[tex]8x+20y=-120[/tex]Rewritting it, we have
[tex]\begin{gathered} 8x+20y=-120 \\ 8x+20y-8x=-120-8x \\ 20y=-8x-120 \\ \frac{20y}{20}=\frac{-8x-120}{20} \\ y=\frac{-8x}{20}-6 \\ y=-\frac{2}{5}x-6 \end{gathered}[/tex]This is our line equation written in slope intercept form.
[tex]y=-\frac{2}{5}x-6[/tex]