Explanation
the equation of a line in slope-intercept point is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Step 1
isolate y
[tex]\begin{gathered} 5x+10y=-10 \\ \text{subtract 5x in both sides} \\ 5x+10y-5x=-10-5x \\ 10y=-10-5x \\ \text{divide both sides by 10} \\ \frac{10y}{10}=-\frac{10}{10}-\frac{5}{10}x \\ y=-1-\frac{1}{2}x \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]then
[tex]\begin{gathered} y=-\frac{1}{2}x-1\rightarrow y=mx+b \\ \text{slope}=-\frac{1}{2} \\ y-\text{intercept}=-1 \end{gathered}[/tex]I hope this helps you
