We have a line with a slope m=-2 and that pass through (3,-1).
The easiest way to get the equation of the line when knowing the slope and one point of the line is to write the equation in point-slope form:
[tex]y-y_0=m(x-x_0)[/tex]
In this case, m=-2 and (x0,y0)=(3,-1), so we can replace and rearrange as:
[tex]\begin{gathered} y-(-1)=-2(x-3) \\ y=-2(x-3)-1 \\ y=-2x+6-1 \\ y=-2x+5 \end{gathered}[/tex]
Answer: y = -2x+5
