Line equations can be written in slope-intercept form, and this form is
[tex]y=mx+b[/tex]
Where m represents the slope and b the y-intercept.
The equation of our line is
[tex]5x+10y=-40[/tex]
To rewrite in slope-intercept form, let's start by subtracting 5x on both sides
[tex]\begin{gathered} 5x+10y-5x=-40-5x \\ 10y=-5x-40 \end{gathered}[/tex]
Now, we just divide both sides by 10
[tex]\begin{gathered} \frac{10y}{10}=-\frac{5x}{10}-\frac{40}{10} \\ y=-\frac{1}{2}x-4 \end{gathered}[/tex]
This is the line equation in slope-intercept form
[tex]y=-\frac{1}{2}x-4[/tex]
